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## Publications of Ingrid Daubechies    :chronological  alphabetical  combined listing:

%% Papers Published
@article{fds341333,
Author = {Shan, S and Kovalsky, SZ and Winchester, JM and Boyer, DM and Daubechies, I},
Title = {ariaDNE: A robustly implemented algorithm for Dirichlet
energy of the normal},
Journal = {Methods in Ecology and Evolution},
Volume = {10},
Number = {4},
Pages = {541-552},
Year = {2019},
Month = {April},
url = {http://dx.doi.org/10.1111/2041-210X.13148},
Abstract = {© 2019 The Authors. Methods in Ecology and Evolution ©
2019 British Ecological Society Shape characterizers are
metrics that quantify aspects of the overall geometry of a
three-dimensional (3D) digital surface. When computed for
biological objects, the values of a shape characterizer are
largely independent of homology interpretations and often
contain a strong ecological and functional signal. Thus,
shape characterizers are useful for understanding
evolutionary processes. Dirichlet normal energy (DNE) is a
widely used shape characterizer in morphological studies.
Recent studies found that DNE is sensitive to various
procedures for preparing 3D mesh from raw scan data, raising
concerns regarding comparability and objectivity when
utilizing DNE in morphological research. We provide a
robustly implemented algorithm for computing the Dirichlet
energy of the normal (ariaDNE) on 3D meshes. We show through
simulation that the effects of preparation-related mesh
surface attributes, such as triangle count, mesh
representation, noise, smoothing and boundary triangles, are
retains the potential of DNE for biological studies,
illustrated by its effectiveness in differentiating species
by dietary preferences. Use of ariaDNE can dramatically
enhance the assessment of the ecological aspects of
morphological variation by its stability under different 3D
model acquisition methods and preparation procedure. Towards
this goal, we provide scripts for computing ariaDNE and
ariaDNE values for specimens used in previously published
DNE analyses.},
Doi = {10.1111/2041-210X.13148},
Key = {fds341333}
}

@article{fds342140,
Author = {Zhu, W and Qiu, Q and Huang, J and Calderbank, R and Sapiro, G and Daubechies, I},
Title = {LDMNet: Low Dimensional Manifold Regularized Neural
Networks},
Journal = {Proceedings of the Ieee Computer Society Conference on
Computer Vision and Pattern Recognition},
Pages = {2743-2751},
Year = {2018},
Month = {December},
url = {http://dx.doi.org/10.1109/CVPR.2018.00290},
Abstract = {© 2018 IEEE. Deep neural networks have proved very
successful on archetypal tasks for which large training sets
are available, but when the training data are scarce, their
performance suffers from overfitting. Many existing methods
of reducing overfitting are data-independent. Data-dependent
regularizations are mostly motivated by the observation that
data of interest lie close to a manifold, which is typically
hard to parametrize explicitly. These methods usually only
focus on the geometry of the input data, and do not
necessarily encourage the networks to produce geometrically
meaningful features. To resolve this, we propose the
Low-Dimensional-Manifold-regularized neural Network
(LDMNet), which incorporates a feature regularization method
that focuses on the geometry of both the input data and the
output features. In LDMNet, we regularize the network by
encouraging the combination of the input data and the output
features to sample a collection of low dimensional
manifolds, which are searched efficiently without explicit
parametrization. To achieve this, we directly use the
manifold dimension as a regularization term in a variational
functional. The resulting Euler-Lagrange equation is a
Laplace-Beltrami equation over a point cloud, which is
solved by the point integral method without increasing the
computational complexity. In the experiments, we show that
LDMNet significantly outperforms widely-used regularizers.
Moreover, LDMNet can extract common features of an object
imaged via different modalities, which is very useful in
real-world applications such as cross-spectral face
recognition.},
Doi = {10.1109/CVPR.2018.00290},
Key = {fds342140}
}

@article{fds340382,
Author = {Yin, R and Daubechies, I},
Title = {Directional Wavelet Bases Constructions with Dyadic Quincunx
Subsampling},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {24},
Number = {3},
Pages = {872-907},
Publisher = {Springer Nature},
Year = {2018},
Month = {June},
url = {http://dx.doi.org/10.1007/s00041-017-9540-z},
construct directional wavelet systems that will enable
building efficient signal representation schemes with good
direction selectivity. In particular, we focus on wavelet
bases with dyadic quincunx subsampling. In our previous work
(Yin, in: Proceedings of the 2015 international conference
on sampling theory and applications (SampTA), 2015), we show
that the supports of orthonormal wavelets in our framework
are discontinuous in the frequency domain, yet this
irregularity constraint can be avoided in frames, even with
redundancy factor <2. In this paper, we focus on the
extension of orthonormal wavelets to biorthogonal wavelets
and show that the same obstruction of regularity as in
orthonormal schemes exists in biorthogonal schemes. In
addition, we provide a numerical algorithm for biorthogonal
wavelets construction where the dual wavelets can be
optimized, though at the cost of deteriorating the primal
wavelets due to the intrinsic irregularity of biorthogonal
schemes.},
Doi = {10.1007/s00041-017-9540-z},
Key = {fds340382}
}

@article{fds329931,
Author = {Gao, T and Yapuncich, GS and Daubechies, I and Mukherjee, S and Boyer,
DM},
Title = {Development and Assessment of Fully Automated and Globally
Transitive Geometric Morphometric Methods, With Application
to a Biological Comparative Dataset With High Interspecific
Variation.},
Journal = {Anatomical Record (Hoboken, N.J. : 2007)},
Volume = {301},
Number = {4},
Pages = {636-658},
Year = {2018},
Month = {April},
url = {http://dx.doi.org/10.1002/ar.23700},
Abstract = {Automated geometric morphometric methods are promising tools
for shape analysis in comparative biology, improving
researchers' abilities to quantify variation extensively (by
permitting more specimens to be analyzed) and intensively
(by characterizing shapes with greater fidelity). Although
use of these methods has increased, published automated
methods have some notable limitations: pairwise
correspondences are frequently inaccurate and pairwise
mappings are not globally consistent (i.e., they lack
transitivity across the full sample). Here, we reassess the
accuracy of published automated methods-cPDist (Boyer et al.
Proc Nat Acad Sci 108 () 18221-18226) and auto3Dgm (Boyer et
al.: Anat Rec 298 () 249-276)-and evaluate several
modifications to these methods. We show that a substantial
percentage of alignments and pairwise maps between specimens
of dissimilar geometries were inaccurate in the study of
Boyer et al. (Proc Nat Acad Sci 108 () 18221-18226), despite
a taxonomically partitioned variance structure of continuous
Procrustes distances. We show these inaccuracies are
remedied using a globally informed methodology within a
collection of shapes, rather than relying on pairwise
comparisons (c.f. Boyer et al.: Anat Rec 298 () 249-276).
Unfortunately, while global information generally enhances
maps between dissimilar objects, it can degrade the quality
of correspondences between similar objects due to the
accumulation of numerical error. We explore a number of
approaches to mitigate this degradation, quantify their
performance, and compare the generated pairwise maps (and
the shape space characterized by these maps) to a "ground
truth" obtained from landmarks manually collected by
geometric morphometricians. Novel methods both improve the
quality of the pairwise correspondences relative to cPDist
and achieve a taxonomic distinctiveness comparable to
auto3Dgm. Anat Rec, 301:636-658, 2018. © 2017 Wiley
Periodicals, Inc.},
Doi = {10.1002/ar.23700},
Key = {fds329931}
}

@article{fds333315,
Author = {Xu, J and Yang, H and Daubechies, I},
Title = {Recursive diffeomorphism-based regression for shape
functions},
Journal = {Siam Journal on Mathematical Analysis},
Volume = {50},
Number = {1},
Pages = {5-32},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1137/16M1097535},
Abstract = {© 2018 Society for Industrial and Applied Mathematics. This
paper proposes a recursive diffeomorphism-based regression
method for the one-dimensional generalized mode
decomposition problem that aims at extracting generalized
modes αk(t)sk(2πNkφk(t)) from their superpositionKk=1
αk(t)sk(2πNkφk(t)). We assume that the instantaneous
information, e.g., αk(t) and Nkφk(t), is determined by,
e.g., a one-dimensional synchrosqueezed transform or some
other methods. Our main contribution is to propose a novel
approach based on diffeomorphisms and nonparametric
regression to estimate wave shape functions sk(t). This
leads to a framework for the generalized mode decomposition
problem under a weak well-separation condition. Numerical
examples of synthetic and real data are provided to
demonstrate the successful application of our
approach.},
Doi = {10.1137/16M1097535},
Key = {fds333315}
}

@article{fds339576,
Author = {Alaifari, R and Daubechies, I and Grohs, P and Yin,
R},
Title = {Stable Phase Retrieval in Infinite Dimensions},
Journal = {Foundations of Computational Mathematics},
Publisher = {Springer Nature America, Inc},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1007/s10208-018-9399-7},
Abstract = {© 2018, The Author(s). The problem of phase retrieval is to
determine a signal f∈ H, with H a Hilbert space, from
intensity measurements | F(ω) | , where F(ω) : = ⟨ f, φ
ω ⟩ are measurements of f with respect to a measurement
system (φω)ω∈Ω⊂H. Although phase retrieval is always
stable in the finite-dimensional setting whenever it is
possible (i.e. injectivity implies stability for the inverse
problem), the situation is drastically different if H is
infinite-dimensional: in that case phase retrieval is never
uniformly stable (Alaifari and Grohs in SIAM J Math Anal
49(3):1895–1911, 2017; Cahill et al. in Trans Am Math Soc
Ser B 3(3):63–76, 2016); moreover, the stability
deteriorates severely in the dimension of the problem
(Cahill et al. 2016). On the other hand, all empirically
observed instabilities are of a certain type: they occur
whenever the function |F| of intensity measurements is
concentrated on disjoint sets D j ⊂ Ω , i.e. when
F=∑j=1kFj where each F j is concentrated on D j (and k≥
2). Motivated by these considerations, we propose a new
paradigm for stable phase retrieval by considering the
problem of reconstructing F up to a phase factor that is not
global, but that can be different for each of the subsets D
j , i.e. recovering F up to the equivalence
F∼∑j=1keiαjFj.We present concrete applications (for
example in audio processing) where this new notion of
stability is natural and meaningful and show that in this
setting stable phase retrieval can actually be achieved, for
instance, if the measurement system is a Gabor frame or a
frame of Cauchy wavelets.},
Doi = {10.1007/s10208-018-9399-7},
Key = {fds339576}
}

@article{fds332858,
Author = {Alaifari, R and Daubechies, I and Grohs, P and Thakur,
G},
Title = {Reconstructing Real-Valued Functions from Unsigned
Coefficients with Respect to Wavelet and Other
Frames},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {23},
Number = {6},
Pages = {1480-1494},
Year = {2017},
Month = {December},
url = {http://dx.doi.org/10.1007/s00041-016-9513-7},
paper we consider the following problem of phase retrieval:
given a collection of real-valued band-limited functions
{ψλ}L2(Rd) that constitutes a semi-discrete frame, we ask
whether any real-valued function f∈ L2(Rd) can be uniquely
recovered from its unsigned convolutions { | f∗ ψλ| }
λ∈Λ. We find that under some mild assumptions on the
semi-discrete frame and if f has exponential decay at ∞,
it suffices to know | f∗ ψλ| on suitably fine lattices
to uniquely determine f (up to a global sign factor). We
further establish a local stability property of our
reconstruction problem. Finally, for two concrete examples
of a (discrete) frame of L2(Rd) , d= 1 , 2 , we show that
through sufficient oversampling one obtains a frame such
that any real-valued function with exponential decay can be
uniquely recovered from its unsigned frame
coefficients.},
Doi = {10.1007/s00041-016-9513-7},
Key = {fds332858}
}

@article{fds325388,
Author = {Deligiannis, N and Mota, JFC and Cornelis, B and Rodrigues, MRD and Daubechies, I},
Title = {Multi-Modal Dictionary Learning for Image Separation With
Application in Art Investigation.},
Journal = {Ieee Transactions on Image Processing : a Publication of the
Ieee Signal Processing Society},
Volume = {26},
Number = {2},
Pages = {751-764},
Year = {2017},
Month = {February},
url = {http://dx.doi.org/10.1109/tip.2016.2623484},
Abstract = {In support of art investigation, we propose a new source
separation method that unmixes a single X-ray scan acquired
from double-sided paintings. In this problem, the X-ray
signals to be separated have similar morphological
characteristics, which brings previous source separation
methods to their limits. Our solution is to use photographs
taken from the front-and back-side of the panel to drive the
separation process. The crux of our approach relies on the
coupling of the two imaging modalities (photographs and
X-rays) using a novel coupled dictionary learning framework
able to capture both common and disparate features across
the modalities using parsimonious representations; the
common component captures features shared by the multi-modal
images, whereas the innovation component captures
modality-specific information. As such, our model enables
the formulation of appropriately regularized convex
optimization procedures that lead to the accurate separation
of the X-rays. Our dictionary learning framework can be
tailored both to a single- and a multi-scale framework, with
the latter leading to a significant performance improvement.
Moreover, to improve further on the visual quality of the
separated images, we propose to train coupled dictionaries
that ignore certain parts of the painting corresponding to
craquelure. Experimentation on synthetic and real data -
taken from digital acquisition of the Ghent Altarpiece
(1432) - confirms the superiority of our method against the
state-of-the-art morphological component analysis technique
that uses either fixed or trained dictionaries to perform
image separation.},
Doi = {10.1109/tip.2016.2623484},
Key = {fds325388}
}

@article{fds328056,
Author = {Fodor, G and Cornelis, B and Yin, R and Dooms, A and Daubechies,
I},
Title = {Cradle removal in X-ray images of panel paintings},
Journal = {Image Processing on Line},
Volume = {7},
Pages = {23-42},
Publisher = {Image Processing On Line},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.5201/ipol.2017.174},
Abstract = {© 2017 IPOL & the authors CC–BY–NC–SA. We address the
problem of mitigating the visually displeasing effects of
cradling in X-ray images of panel paintings. The proposed
algorithm consists of three stages. In the first stage the
location of the cradling is detected semi-automatically and
the grayscale inconsistency, caused by the thickness of the
source separation method to decompose the X-ray image into a
so-called cartoon part and a texture part, where the latter
contains mostly the wood grain from both the panel as well
as the cradling. In the third and final stage the algorithm
tries to learn the distinction between the texture patterns
that originate from the cradling and those from other
components such as the panel and/or the painting. The goal
of the proposed research is to improve the readability of
X-ray images of paintings for art experts.},
Doi = {10.5201/ipol.2017.174},
Key = {fds328056}
}

@article{fds324089,
Author = {Cornelis, B and Yang, H and Goodfriend, A and Ocon, N and Lu, J and Daubechies, I},
Title = {Removal of Canvas Patterns in Digital Acquisitions of
Paintings.},
Journal = {Ieee Transactions on Image Processing : a Publication of the
Ieee Signal Processing Society},
Volume = {26},
Number = {1},
Pages = {160-171},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1109/tip.2016.2621413},
Abstract = {We address the removal of canvas artifacts from
high-resolution digital photographs and X-ray images of
paintings on canvas. Both imaging modalities are common
investigative tools in art history and art conservation.
Canvas artifacts manifest themselves very differently
according to the acquisition modality; they can hamper the
visual reading of the painting by art experts, for instance,
in preparing a restoration campaign. Computer-aided canvas
removal is desirable for restorers when the painting on
canvas they are preparing to restore has acquired over the
years a much more salient texture. We propose a new
algorithm that combines a cartoon-texture decomposition
method with adaptive multiscale thresholding in the
frequency domain to isolate and suppress the canvas
components. To illustrate the strength of the proposed
method, we provide various examples, for acquisitions in
both imaging modalities, for paintings with different types
of canvas and from different periods. The proposed algorithm
outperforms previous methods proposed for visual photographs
such as morphological component analysis and Wiener
filtering and it also works for the digital removal of
canvas artifacts in X-ray images.},
Doi = {10.1109/tip.2016.2621413},
Key = {fds324089}
}

@article{fds329099,
Author = {Voronin, S and Daubechies, I},
Title = {An iteratively reweighted least squares algorithm for sparse
regularization},
Volume = {693},
Pages = {391-411},
Booktitle = {Contemporary Mathematics},
Publisher = {American Mathematical Society},
Year = {2017},
Month = {January},
ISBN = {9781470428365},
url = {http://dx.doi.org/10.1090/conm/693/13941},
Abstract = {© 2017 by the authors. We present a new algorithm and the
corresponding convergence analysis for the regularization of
linear inverse problems with sparsity constraints, applied
to a new generalized sparsity promoting functional. The
algorithm is based on the idea of iteratively reweighted
least squares, reducing the minimization at every iteration
step to that of a functional including only ℓ2 -norms.
This amounts to smoothing of the absolute value function
that appears in the generalized sparsity promoting penalty
we consider, with the smoothing becoming iteratively less
pronounced. We demonstrate that the sequence of iterates of
our algorithm converges to a limit that minimizes the
original functional.},
Doi = {10.1090/conm/693/13941},
Key = {fds329099}
}

@article{fds327595,
Author = {Yin, R and Gao, T and Lu, YM and Daubechies, I},
Title = {A tale of two bases: Local-nonlocal regularization on image
patches with convolution framelets},
Journal = {Siam Journal on Imaging Sciences},
Volume = {10},
Number = {2},
Pages = {711-750},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1137/16M1091447},
Abstract = {© 2017 Rujie Yin. We propose an image representation scheme
combining the local and nonlocal characterization of patches
in an image. Our representation scheme can be shown to be
equivalent to a tight frame constructed from convolving
local bases (e.g., wavelet frames, discrete cosine
transforms, etc.) with nonlocal bases (e.g., spectral basis
induced by nonlinear dimension reduction on patches), and we
call the resulting frame elements convolution framelets.
Insight gained from analyzing the proposed representation
leads to a novel interpretation of a recent high-performance
patch-based image processing algorithm using the point
integral method (PIM) and the low dimensional manifold model
(LDMM) [S. Osher, Z. Shi, and W. Zhu, Low Dimensional
Manifold Model for Image Processing, Tech. Rep., CAM report
16-04, UCLA, Los Angeles, CA, 2016]. In particular, we show
that LDMM is a weighted ℓ2-regularization on the
coefficients obtained by decomposing images into linear
combinations of convolution framelets; based on this
understanding, we extend the original LDMM to a reweighted
version that yields further improved results. In addition,
we establish the energy concentration property of
convolution framelet coefficients for the setting where the
local basis is constructed from a given nonlocal basis via a
linear reconstruction framework; a generalization of this
framework to unions of local embeddings can provide a
natural setting for interpreting BM3D, one of the
state-of-the-art image denoising algorithms.},
Doi = {10.1137/16M1091447},
Key = {fds327595}
}

@article{fds318286,
Author = {Wu, H-T and Lewis, GF and Davila, MI and Daubechies, I and Porges,
SW},
Title = {Optimizing Estimates of Instantaneous Heart Rate from Pulse
Wave Signals with the Synchrosqueezing Transform.},
Journal = {Methods of Information in Medicine},
Volume = {55},
Number = {5},
Pages = {463-472},
Year = {2016},
Month = {October},
url = {http://dx.doi.org/10.3414/me16-01-0026},
Abstract = {With recent advances in sensor and computer technologies,
the ability to monitor peripheral pulse activity is no
longer limited to the laboratory and clinic. Now inexpensive
sensors, which interface with smartphones or other
computer-based devices, are expanding into the consumer
market. When appropriate algorithms are applied, these new
technologies enable ambulatory monitoring of dynamic
physiological responses outside the clinic in a variety of
applications including monitoring fatigue, health, workload,
fitness, and rehabilitation. Several of these applications
rely upon measures derived from peripheral pulse waves
measured via contact or non-contact photoplethysmography
(PPG). As technologies move from contact to non-contact PPG,
there are new challenges. The technology necessary to
estimate average heart rate over a few seconds from a
noncontact PPG is available. However, a technology to
precisely measure instantaneous heat rate (IHR) from
non-contact sensors, on a beat-to-beat basis, is more
challenging.The objective of this paper is to develop an
algorithm with the ability to accurately monitor IHR from
peripheral pulse waves, which provides an opportunity to
measure the neural regulation of the heart from the
beat-to-beat heart rate pattern (i.e., heart rate
variability).The adaptive harmonic model is applied to model
the contact or non-contact PPG signals, and a new
methodology, the Synchrosqueezing Transform (SST), is
applied to extract IHR. The body sway rhythm inherited in
the non-contact PPG signal is modeled and handled by the
notion of wave-shape function.The SST optimizes the
extraction of IHR from the PPG signals and the technique
functions well even during periods of poor signal to noise.
We contrast the contact and non-contact indices of PPG
derived heart rate with a criterion electrocardiogram (ECG).
ECG and PPG signals were monitored in 21 healthy subjects
performing tasks with different physical demands. The root
mean square error of IHR estimated by SST is significantly
better than commonly applied methods such as autoregressive
(AR) method. In the walking situation, while AR method
fails, SST still provides a reasonably good result.The SST
processed PPG data provided an accurate estimate of the ECG
derived IHR and consistently performed better than commonly
applied methods such as autoregressive method.},
Doi = {10.3414/me16-01-0026},
Key = {fds318286}
}

@article{fds320873,
Author = {O'Neal, WT and Wang, YG and Wu, H-T and Zhang, Z-M and Li, Y and Tereshchenko, LG and Estes, EH and Daubechies, I and Soliman,
EZ},
Title = {Electrocardiographic J Wave and Cardiovascular Outcomes in
the General Population (from the Atherosclerosis Risk In
Communities Study).},
Journal = {The American Journal of Cardiology},
Volume = {118},
Number = {6},
Pages = {811-815},
Year = {2016},
Month = {September},
url = {http://dx.doi.org/10.1016/j.amjcard.2016.06.047},
Abstract = {The association between the J wave, a key component of the
early repolarization pattern, and adverse cardiovascular
outcomes remains unclear. Inconsistencies have stemmed from
the different methods used to measure the J wave. We
examined the association between the J wave, detected by an
automated method, and adverse cardiovascular outcomes in
14,592 (mean age = 54 ± 5.8 years; 56% women; 26% black)
participants from the Atherosclerosis Risk In Communities
(ARIC) study. The J wave was detected at baseline (1987 to
1989) and during follow-up study visits (1990 to 1992, 1993
to 1995, and 1996 to 1998) using a fully automated method.
Sudden cardiac death, coronary heart disease death, and
cardiovascular mortality were ascertained from hospital
discharge records, death certificates, and autopsy data
through December 31, 2010. A total of 278 participants
(1.9%) had evidence of a J wave. Over a median follow-up of
22 years, 4,376 of the participants (30%) died. In a
multivariable Cox regression analysis adjusted for
demographics, cardiovascular risk factors, and potential
confounders, the J wave was not associated with an increased
risk of sudden cardiac death (hazard ratio [HR] 0.74, 95% CI
0.36 to 1.50), coronary heart disease death (HR 0.72, 95% CI
0.40 to 1.32), or cardiovascular mortality (HR 1.16, 95% CI
0.87 to 1.56). An interaction was detected for
cardiovascular mortality by gender with men (HR 1.54, 95% CI
1.09 to 2.19) having a stronger association than women (HR
0.74, 95% CI 0.43 to 1.25; P-interaction = 0.030). In
conclusion, our findings suggest that the J wave is a benign
entity that is not associated with an increased risk for
sudden cardiac arrest in middle-aged adults in the United
States.},
Doi = {10.1016/j.amjcard.2016.06.047},
Key = {fds320873}
}

@article{fds318287,
Author = {Yin, R and Cornelis, B and Fodor, G and Ocon, N and Dunson, D and Daubechies, I},
Title = {Removing cradle artifacts in X-ray images of
paintings},
Journal = {Siam Journal on Imaging Sciences},
Volume = {9},
Number = {3},
Pages = {1247-1272},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2016},
Month = {August},
url = {http://dx.doi.org/10.1137/15M1053554},
Abstract = {© 2016 Rujie Yin. We propose an algorithm that removes the
visually unpleasant effects of cradling in X-ray images of
panel paintings, with the goal of improving the X-ray image
readability by art experts. The algorithm consists of three
stages. In the first stage the location of the cradle is
detected automatically and the grayscale inconsistency,
caused by the thickness of the cradle, is corrected. In a
second stage we use a method called morphological component
analysis to separate the X-ray image into a so-called
cartoon part and a texture part, where the latter contains
mostly the wood grain from both the panel and the cradling.
The algorithm next learns a Bayesian factor model that
distinguishes between the texture patterns that originate
from the cradle and those from other components such as the
panel and/or the painting on the panel surface, and finally
uses this to remove the textures associated with the cradle.
We apply the algorithm to a number of historically important
paintings on panel. We also show how it can be used to
digitally remove stretcher artifacts from X-rays of
paintings on canvas. We compare our results with those
obtained manually by best current practices in art
conservation as well as on a ground truth dataset,
consisting of X-ray images of a painting before and after
removal of the physically attached cradle.},
Doi = {10.1137/15M1053554},
Key = {fds318287}
}

@article{fds323650,
Author = {Daubechies, I and Defrise, M and De Mol and C},
Title = {Sparsity-enforcing regularisation and ISTA
revisited},
Journal = {Inverse Problems},
Volume = {32},
Number = {10},
Pages = {104001-104001},
Publisher = {IOP Publishing},
Year = {2016},
Month = {August},
url = {http://dx.doi.org/10.1088/0266-5611/32/10/104001},
concept of sparsity emerged in different disciplines such as
statistics, imaging, signal processing and inverse problems,
and proved to be useful for several applications.
Sparsity-enforcing constraints or penalties were then shown
to provide a viable alternative to the usual quadratic ones
for the regularisation of ill-posed problems. To compute the
corresponding regularised solutions, a simple, iterative and
provably convergent algorithm was proposed and later on
referred to as the iterative soft-thresholding algorithm.
This paper provides a brief review of these early results as
well as that of the subsequent literature, albeit from the
authors' limited perspective. It also presents the
previously unpublished proof of an extension of the original
framework.},
Doi = {10.1088/0266-5611/32/10/104001},
Key = {fds323650}
}

@article{fds321988,
Author = {Deligiannis, N and Mota, JFC and Cornelis, B and Rodrigues, MRD and Daubechies, I},
Title = {X-ray image separation via coupled dictionary
learning},
Journal = {Proceedings International Conference on Image Processing,
Icip},
Volume = {2016-August},
Pages = {3533-3537},
Publisher = {IEEE},
Year = {2016},
Month = {August},
ISBN = {9781467399616},
url = {http://dx.doi.org/10.1109/ICIP.2016.7533017},
Abstract = {© 2016 IEEE. In support of art investigation, we propose a
new source separation method that unmixes a single X-ray
scan acquired from double-sided paintings. Unlike prior
source separation methods, which are based on statistical or
structural incoherence of the sources, we use visual images
taken from the front- and back-side of the panel to drive
the separation process. The coupling of the two imaging
modalities is achieved via a new multi-scale dictionary
learning method. Experimental results demonstrate that our
method succeeds in the discrimination of the sources, while
state-of-the-art methods fail to do so.},
Doi = {10.1109/ICIP.2016.7533017},
Key = {fds321988}
}

@article{fds317216,
Author = {Yin, R and Monson, E and Honig, E and Daubechies, I and Maggioni,
M},
Title = {Object recognition in art drawings: Transfer of a neural
network},
Journal = {2015 Ieee International Conference on Acoustics, Speech, and
Signal Processing (Icassp)},
Volume = {2016-May},
Pages = {2299-2303},
Publisher = {IEEE},
Year = {2016},
Month = {May},
ISBN = {9781479999880},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2016.7472087},
Abstract = {© 2016 IEEE. We consider the problem of recognizing objects
in collections of art works, in view of automatically
labeling, searching and organizing databases of art works.
To avoid manually labelling objects, we introduce a
framework for transferring a convolutional neural network
(CNN), trained on available large collections of labelled
natural images, to the context of drawings. We retrain both
the top and the bottom layer of the network, responsible for
the high-level classiication output and the low-level
features detection respectively, by transforming natural
images into drawings. We apply this procedure to the
drawings in the Jan Brueghel Wiki, and show the transferred
CNN learns a discriminative metric on drawings and achieves
good recognition accuracy. We also discuss why standard
descriptor-based methods is problematic in the context of
drawings.},
Doi = {10.1109/ICASSP.2016.7472087},
Key = {fds317216}
}

@article{fds315774,
Author = {Daubechies, I and Wang, YG and Wu, H-T},
Title = {ConceFT: concentration of frequency and time via a
multitapered synchrosqueezed transform.},
Journal = {Philosophical Transactions. Series A, Mathematical,
Physical, and Engineering Sciences},
Volume = {374},
Number = {2065},
Pages = {20150193},
Year = {2016},
Month = {April},
ISSN = {1364-503X},
url = {http://dx.doi.org/10.1098/rsta.2015.0193},
Abstract = {A new method is proposed to determine the time-frequency
content of time-dependent signals consisting of multiple
oscillatory components, with time-varying amplitudes and
instantaneous frequencies. Numerical experiments as well as
a theoretical analysis are presented to assess its
effectiveness.},
Doi = {10.1098/rsta.2015.0193},
Key = {fds315774}
}

@article{fds315775,
Author = {Huang, NE and Daubechies, I and Hou, TY},
Title = {Adaptive data analysis: theory and applications.},
Journal = {Philosophical Transactions. Series A, Mathematical,
Physical, and Engineering Sciences},
Volume = {374},
Number = {2065},
Pages = {20150207},
Year = {2016},
Month = {April},
ISSN = {1364-503X},
url = {http://dx.doi.org/10.1098/rsta.2015.0207},
Doi = {10.1098/rsta.2015.0207},
Key = {fds315775}
}

@article{fds287094,
Author = {Daubechies, I and Saab, R},
Title = {A Deterministic Analysis of Decimation for Sigma-Delta
Quantization of Bandlimited Functions},
Journal = {Ieee Signal Processing Letters},
Volume = {22},
Number = {11},
Pages = {2093-2096},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2015},
Month = {November},
ISSN = {1070-9908},
url = {http://dx.doi.org/10.1109/LSP.2015.2459758},
Abstract = {© 2015 IEEE. We study Sigma-Delta (Σ Δ) quantization of
oversampled bandlimited functions. We prove that digitally
integrating blocks of bits and then down-sampling, a process
known as decimation, can efficiently encode the associated
Σ Δ bit-stream. It allows a large reduction in the
bit-rate while still permitting good approximation of the
underlying bandlimited function via an appropriate
reconstruction kernel. Specifically, in the case of stable
rth order Σ Δ schemes we show that the reconstruction
error decays exponentially in the bit-rate. For example,
this result applies to the 1-bit, greedy, first-order Σ Δ
scheme.},
Doi = {10.1109/LSP.2015.2459758},
Key = {fds287094}
}

@article{fds287095,
Author = {Yang, H and Lu, J and Brown, WP and Daubechies, I and Ying,
L},
Title = {Quantitative canvas weave analysis using 2-D synchrosqueezed
transforms: Application of time-frequency analysis to art
investigation},
Journal = {Ieee Signal Processing Magazine},
Volume = {32},
Number = {4},
Pages = {55-63},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2015},
Month = {July},
ISSN = {1053-5888},
url = {http://hdl.handle.net/10161/12009 Duke open
access},
Abstract = {© 1991-2012 IEEE. Quantitative canvas weave analysis has
many applications in art investigations of paintings,
including dating, forensics, and canvas rollmate
identification [1]?[3]. Traditionally, canvas analysis is
based on X-radiographs. Prior to serving as a painting
canvas, a piece of fabric is coated with a priming agent;
smoothing its surface makes this layer thicker between and
thinner right on top of weave threads. These variations
affect the X-ray absorption, making the weave pattern stand
out in X-ray images of the finished painting. To
characterize this pattern, it is customary to visually
inspect small areas within the X-radiograph and count the
number of horizontal and vertical weave threads; averages of
these then estimate the overall canvas weave density. The
tedium of this process typically limits its practice to just
a few sample regions of the canvas. In addition, it does not
capture more subtle information beyond weave density, such
as thread angles or variations in the weave pattern. Signal
processing techniques applied to art investigation are now
increasingly used to develop computer-assisted canvas weave
analysis tools.},
Doi = {10.1109/MSP.2015.2406882},
Key = {fds287095}
}

@article{fds287096,
Author = {Pizurica, A and Platisa, L and Ruzic, T and Cornelis, B and Dooms, A and Martens, M and Dubois, H and Devolder, B and De Mey and M and Daubechies,
I},
Title = {Digital image processing of the ghent altarpiece: Supporting
the painting's study and conservation treatment},
Journal = {Ieee Signal Processing Magazine},
Volume = {32},
Number = {4},
Pages = {112-122},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2015},
Month = {July},
ISSN = {1053-5888},
url = {http://dx.doi.org/10.1109/MSP.2015.2411753},
Abstract = {© 2015 IEEE. Hanging in the Saint Bavo Cathedral in Ghent,
Belgium, is The Ghent Altarpiece, also known as The
Adoration of the Mystic Lamb (see Figure 1). According to an
inscription on the outer frames, it was painted by brothers
Hubert and Jan van Eyck for Joos Vijd and?his wife Elisabeth
Borluut in 1432. It is one of the most admired and
influential paintings in the history of art and has given
rise to many intriguing questions that have been puzzling
art historians to date [11]. Moreover, the material history
of the panels is very complicated. They were hidden,
dismantled, moved away, stolen, and recovered during riots,
fires and wars. The recovery of the panels by the U.S. Army
in the Nazi hoards deep in the Altaussee salt mines has
particularly marked memories. One panel was stolen in 1934
and never recovered. Besides varying conservation
conditions, the panels underwent numerous restoration
treatments and were even partially painted
over.},
Doi = {10.1109/MSP.2015.2411753},
Key = {fds287096}
}

@article{fds303541,
Author = {Polatkan, G and Zhou, M and Carin, L and Blei, D and Daubechies,
I},
Title = {A Bayesian Nonparametric Approach to Image
Super-Resolution.},
Journal = {Ieee Transactions on Pattern Analysis and Machine
Intelligence},
Volume = {37},
Number = {2},
Pages = {346-358},
Year = {2015},
Month = {February},
url = {http://arxiv.org/abs/1209.5019v1},
Abstract = {Super-resolution methods form high-resolution images from
low-resolution images. In this paper, we develop a new
Bayesian nonparametric model for super-resolution. Our
method uses a beta-Bernoulli process to learn a set of
recurring visual patterns, called dictionary elements, from
the data. Because it is nonparametric, the number of
elements found is also determined from the data. We test the
results on both benchmark and natural images, comparing with
several other models from the research literature. We
perform large-scale human evaluation experiments to assess
the visual quality of the results. In a first
implementation, we use Gibbs sampling to approximate the
posterior. However, this algorithm is not feasible for
large-scale data. To circumvent this, we then develop an
online variational Bayes (VB) algorithm. This algorithm
finds high quality dictionaries in a fraction of the time
needed by the Gibbs sampler.},
Doi = {10.1109/tpami.2014.2321404},
Key = {fds303541}
}

@article{fds287098,
Author = {Boyer, DM and Puente, J and Gladman, JT and Glynn, C and Mukherjee, S and Yapuncich, GS and Daubechies, I},
Title = {A new fully automated approach for aligning and comparing
shapes.},
Journal = {Anatomical Record (Hoboken, N.J. : 2007)},
Volume = {298},
Number = {1},
Pages = {249-276},
Year = {2015},
Month = {January},
ISSN = {1932-8486},
url = {http://dx.doi.org/10.1002/ar.23084},
Abstract = {Three-dimensional geometric morphometric (3DGM) methods for
placing landmarks on digitized bones have become
increasingly sophisticated in the last 20 years, including
greater degrees of automation. One aspect shared by all 3DGM
methods is that the researcher must designate initial
landmarks. Thus, researcher interpretations of homology and
correspondence are required for and influence
representations of shape. We present an algorithm allowing
fully automatic placement of correspondence points on
samples of 3D digital models representing bones of different
individuals/species, which can then be input into standard
3DGM software and analyzed with dimension reduction
techniques. We test this algorithm against several samples,
primarily a dataset of 106 primate calcanei represented by
1,024 correspondence points per bone. Results of our
automated analysis of these samples are compared to a
published study using a traditional 3DGM approach with 27
landmarks on each bone. Data were analyzed with
morphologika(2.5) and PAST. Our analyses returned strong
correlations between principal component scores, similar
variance partitioning among components, and similarities
between the shape spaces generated by the automatic and
traditional methods. While cluster analyses of both
automatically generated and traditional datasets produced
broadly similar patterns, there were also differences.
Overall these results suggest to us that automatic
quantifications can lead to shape spaces that are as
meaningful as those based on observer landmarks, thereby
presenting potential to save time in data collection,
increase completeness of morphological quantification,
eliminate observer error, and allow comparisons of shape
diversity between different types of bones. We provide an R
package for implementing this analysis.},
Doi = {10.1002/ar.23084},
Key = {fds287098}
}

@article{fds287099,
Author = {Wang, YG and Wu, H-T and Daubechies, I and Li, Y and Estes, EH and Soliman,
EZ},
Title = {Automated J wave detection from digital 12-lead
electrocardiogram.},
Journal = {Journal of Electrocardiology},
Volume = {48},
Number = {1},
Pages = {21-28},
Year = {2015},
Month = {January},
ISSN = {0022-0736},
url = {http://dx.doi.org/10.1016/j.jelectrocard.2014.10.006},
Abstract = {In this report we provide a method for automated detection
of J wave, defined as a notch or slur in the descending
slope of the terminal positive wave of the QRS complex,
using signal processing and functional data analysis
techniques. Two different sets of ECG tracings were selected
from the EPICARE ECG core laboratory, Wake Forest School of
Medicine, Winston Salem, NC. The first set was a training
set comprised of 100 ECGs of which 50 ECGs had J-wave and
the other 50 did not. The second set was a test set (n=116
ECGs) in which the J-wave status (present/absent) was only
known by the ECG Center staff. All ECGs were recorded using
GE MAC 1200 (GE Marquette, Milwaukee, Wisconsin) at 10mm/mV
calibration, speed of 25mm/s and 500HZ sampling rate. All
ECGs were initially inspected visually for technical errors
and inadequate quality, and then automatically processed
with the GE Marquette 12-SL program 2001 version (GE
Marquette, Milwaukee, WI). We excluded ECG tracings with
major abnormalities or rhythm disorder. Confirmation of the
presence or absence of a J wave was done visually by the ECG
Center staff and verified once again by three of the
coauthors. There was no disagreement in the identification
of the J wave state. The signal processing and functional
data analysis techniques applied to the ECGs were conducted
at Duke University and the University of Toronto. In the
training set, the automated detection had sensitivity of
100% and specificity of 94%. For the test set, sensitivity
was 89% and specificity was 86%. In conclusion, test results
of the automated method we developed show a good J wave
detection accuracy, suggesting possible utility of this
approach for defining and detection of other complex ECG
waveforms.},
Doi = {10.1016/j.jelectrocard.2014.10.006},
Key = {fds287099}
}

@article{fds300272,
Author = {A. Pizurica and L. Platisa and T. Ruzic and B. Cornelis and A. Dooms and M.
Martens, H. Dubois and B. Devolder and M. De Mey and I.
Daubechies},
Title = {Digital Image Processing of The Ghent Altarpiece: Supporting
the painting's study and conservation treatment},
Journal = {IEEE Signal Processing Magazine},
Volume = {32},
Pages = {112-122},
Publisher = {IEEE},
Year = {2015},
Key = {fds300272}
}

@article{fds287101,
Author = {Wu, H-T and Hseu, S-S and Bien, M-Y and Kou, YR and Daubechies,
I},
Title = {Evaluating physiological dynamics via synchrosqueezing:
prediction of ventilator weaning.},
Journal = {Ieee Transactions on Bio Medical Engineering},
Volume = {61},
Number = {3},
Pages = {736-744},
Year = {2014},
Month = {March},
ISSN = {0018-9294},
url = {http://dx.doi.org/10.1109/tbme.2013.2288497},
Abstract = {Oscillatory phenomena abound in many types of signals.
Identifying the individual oscillatory components that
constitute an observed biological signal leads to profound
understanding about the biological system. The instantaneous
frequency (IF), the amplitude modulation (AM), and their
temporal variability are widely used to describe these
oscillatory phenomena. In addition, the shape of the
oscillatory pattern, repeated in time for an oscillatory
component, is also an important characteristic that can be
parametrized appropriately. These parameters can be viewed
as phenomenological surrogates for the hidden dynamics of
the biological system. To estimate jointly the IF, AM, and
shape, this paper applies a novel and robust time-frequency
analysis tool, referred to as the synchrosqueezing transform
(SST). The usefulness of the model and SST are shown
directly in predicting the clinical outcome of ventilator
weaning. Compared with traditional respiration parameters,
the breath-to-breath variability has been reported to be a
better predictor of the outcome of the weaning procedure. So
far, however, all these indices normally require at least 20
min of data acquisition to ensure predictive power.
Moreover, the robustness of these indices to the inevitable
noise is rarely discussed. We find that based on the
proposed model, SST and only 3 min of respiration data, the
ROC area under curve of the prediction accuracy is 0.76. The
high predictive power that is achieved in the weaning
problem, despite a shorter evaluation period, and the
stability to noise suggest that other similar kinds of
signal may likewise benefit from the proposed model and
SST.},
Doi = {10.1109/tbme.2013.2288497},
Key = {fds287101}
}

@article{fds287097,
Author = {Yin, R and Dunson, D and Cornelis, B and Brown, B and Ocon, N and Daubechies, I},
Title = {Digital cradle removal in X-ray images of art
paintings},
Journal = {2014 Ieee International Conference on Image Processing, Icip
2014},
Pages = {4299-4303},
Publisher = {IEEE},
Year = {2014},
Month = {January},
ISBN = {9781479957514},
url = {http://dx.doi.org/10.1109/ICIP.2014.7025873},
Abstract = {© 2014 IEEE. We introduce an algorithm that removes the
deleterious effect of cradling on X-ray images of paintings
on wooden panels. The algorithm consists of a three stage
procedure. Firstly, the cradled regions are located
automatically. The second step consists of separating the
X-ray image into a textural and image component. In the last
step the algorithm learns to distinguish between the texture
caused by the wooden cradle and the texture belonging to the
original painted wooden panel. The results obtained with our
method are compared with those obtained manually by best
current practice.},
Doi = {10.1109/ICIP.2014.7025873},
Key = {fds287097}
}

@article{fds303539,
Author = {Cornelis, B and Yang, Y and Vogelstein, JT and Dooms, A and Daubechies,
I and Dunson, D},
Title = {Bayesian crack detection in ultra high resolution multimodal
images of paintings},
Journal = {2013 18th International Conference on Digital Signal
Processing, Dsp 2013},
Year = {2013},
Month = {December},
url = {http://arxiv.org/abs/1304.5894v2},
Abstract = {The preservation of our cultural heritage is of paramount
importance. Thanks to recent developments in digital
acquisition techniques, powerful image analysis algorithms
are developed which can be useful non-invasive tools to
assist in the restoration and preservation of art. In this
paper we propose a semi-supervised crack detection method
that can be used for high-dimensional acquisitions of
paintings coming from different modalities. Our dataset
consists of a recently acquired collection of images of the
Ghent Altarpiece (1432), one of Northern Europe's most
important art masterpieces. Our goal is to build a
classifier that is able to discern crack pixels from the
background consisting of non-crack pixels, making optimal
use of the information that is provided by each modality. To
accomplish this we employ a recently developed
non-parametric Bayesian classifier, that uses tensor
factorizations to characterize any conditional probability.
A prior is placed on the parameters of the factorization
such that every possible interaction between predictors is
allowed while still identifying a sparse subset among these
predictors. The proposed Bayesian classifier, which we will
refer to as conditional Bayesian tensor factorization or
CBTF, is assessed by visually comparing classification
results with the Random Forest (RF) algorithm. © 2013
IEEE.},
Doi = {10.1109/ICDSP.2013.6622710},
Key = {fds303539}
}

@article{fds287100,
Author = {Wu, T and Polatkan, G and Steel, D and Brown, W and Daubechies, I and Calderbank, R},
Title = {Painting analysis using wavelets and probabilistic topic
models},
Journal = {2013 Ieee International Conference on Image Processing, Icip
2013 Proceedings},
Pages = {3264-3268},
Publisher = {IEEE},
Year = {2013},
Month = {December},
url = {http://dx.doi.org/10.1109/ICIP.2013.6738672},
Abstract = {In this paper, computer-based techniques for stylistic
analysis of paintings are applied to the five panels of the
14th century Peruzzi Altarpiece by Giotto di Bondone.
Features are extracted by combining a dual-tree complex
wavelet transform with a hidden Markov tree (HMT) model.
Hierarchical clustering is used to identify stylistic
keywords in image patches, and keyword frequencies are
calculated for sub-images that each contains many patches. A
generative hierarchical Bayesian model learns stylistic
patterns of keywords; these patterns are then used to
characterize the styles of the sub-images; this in turn,
permits to discriminate between paintings. Results suggest
that such unsupervised probabilistic topic models can be
useful to distill characteristic elements of style. © 2013
IEEE.},
Doi = {10.1109/ICIP.2013.6738672},
Key = {fds287100}
}

@article{fds287104,
Author = {Charléty, J and Voronin, S and Nolet, G and Loris, I and Simons, FJ and Sigloch, K and Daubechies, IC},
Title = {Global seismic tomography with sparsity constraints:
Comparison with smoothing and damping regularization},
Journal = {Journal of Geophysical Research},
Volume = {118},
Number = {9},
Pages = {4887-4899},
Publisher = {American Geophysical Union (AGU)},
Year = {2013},
Month = {October},
ISSN = {0148-0227},
url = {http://dx.doi.org/10.1002/jgrb.50326},
Abstract = {We present a realistic application of an inversion scheme
for global seismic tomography that uses as prior information
the sparsity of a solution, defined as having few nonzero
coefficients under the action of a linear transformation. In
this paper, the sparsifying transform is a wavelet
transform. We use an accelerated iterative soft-thresholding
algorithm for a regularization strategy, which produces
sparse models in the wavelet domain. The approach and scheme
we present may be of use for preserving sharp edges in a
tomographic reconstruction and minimizing the number of
features in the solution warranted by the data. The method
is tested on a data set of time delays for finite-frequency
tomography using the USArray network, the first application
in global seismic tomography to real data. The approach
presented should also be suitable for other imaging
problems. From a comparison with a more traditional
inversion using damping and smoothing constraints, we show
that (1) we generally retrieve similar features, (2) fewer
nonzero coefficients under a properly chosen representation
(such as wavelets) are needed to explain the data at the
same level of root-mean-square misfit, (3) the model is
sparse or compressible in the wavelet domain, and (4) we do
not need to construct a heterogeneous mesh to capture the
available resolution. Key Points Global tomography with
solution sparsity in a certain basis as prior
informationOne-norm of model wavelet coefficients as
constraint regularizes the inversionFirst realistic
application on actual data for global seismic tomography. ©
2013 American Geophysical Union. All Rights
Reserved.},
Doi = {10.1002/jgrb.50326},
Key = {fds287104}
}

@article{fds287209,
Author = {Al-Aifari, R and Daubechies, I and Lipman, Y},
Title = {Continuous Procrustes distance between two
surfaces},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {66},
Number = {6},
Pages = {934-964},
Publisher = {WILEY},
Year = {2013},
Month = {June},
url = {http://dx.doi.org/10.1002/cpa.21444},
Abstract = {The Procrustes distance is used to quantify the similarity
or dissimilarity of (three-dimensional) shapes and
extensively used in biological morphometrics. Typically each
(normalized) shape is represented by N landmark points,
chosen to be homologous, as far as possible, and the
Procrustes distance is then computed as $\inf_{R}\sum_{j=1}^N \|Rx_j-x'_j\|^2$, where the minimization is over all
euclidean transformations, and the correspondences $x_j \leftrightarrow x'_j$ are picked in an optimal way. The
discrete Procrustes distance has the drawback that each
shape is represented by only a finite number of points,
which may not capture all the geometric aspects of interest;
a need has been expressed for alternatives that are still
easy to compute. We propose in this paper the concept of
continuous Procrustes distance and prove that it provides a
true metric for two-dimensional surfaces embedded in three
dimensions. We also propose an efficient algorithm to
calculate approximations to this new distance. © 2013 Wiley
Periodicals, Inc.},
Doi = {10.1002/cpa.21444},
Key = {fds287209}
}

@article{fds287200,
Author = {Cornelis, B and Ružić, T and Gezels, E and Dooms, A and Pižurica, A and Platiša, L and Cornelis, J and Martens, M and De Mey and M and Daubechies,
I},
Title = {Crack detection and inpainting for virtual restoration of
paintings: The case of the Ghent Altarpiece},
Journal = {Signal Processing},
Volume = {93},
Number = {3},
Pages = {605-619},
Publisher = {Elsevier BV},
Year = {2013},
Month = {March},
ISSN = {0165-1684},
url = {http://www.sciencedirect.com/science/article/pii/S0165168412002526},
Abstract = {Digital image processing is proving to be of great help in
the analysis and documentation of our vast cultural
heritage. In this paper, we present a new method for the
virtual restoration of digitized paintings with special
attention for the Ghent Altarpiece (1432), a large polyptych
panel painting of which very few digital reproductions
exist. We achieve our objective by detecting and digitally
removing cracks. The detection of cracks is particularly
difficult because of the varying content features in
different parts of the polyptych. Three new detection
methods are proposed and combined in order to detect cracks
of different sizes as well as varying brightness.
Semi-supervised clustering based post-processing is used to
remove objects falsely labelled as cracks. For the
subsequent inpainting stage, a patch-based technique is
applied to handle the noisy nature of the images and to
increase the performance for crack removal. We demonstrate
the usefulness of our method by means of a case study where
the goal is to improve readability of the depiction of text
in a book, present in one of the panels, in order to assist
paleographers in its deciphering. © 2012 Elsevier
B.V.},
Doi = {10.1016/j.sigpro.2012.07.022},
Key = {fds287200}
}

@article{fds287203,
Author = {Anitha, A and Brasoveanu, A and Duarte, M and Hughes, S and Daubechies,
I and Dik, J and Janssens, K and Alfeld, M},
Title = {Restoration of X-ray fluorescence images of hidden
paintings},
Journal = {Signal Processing},
Volume = {93},
Number = {3},
Pages = {592-604},
Publisher = {Elsevier BV},
Year = {2013},
Month = {March},
ISSN = {0165-1684},
url = {http://dx.doi.org/10.1016/j.sigpro.2012.09.027},
Abstract = {This paper describes our methods for repairing and restoring
images of hidden paintings (paintings that have been painted
over and are now covered by a new surface painting) that
have been obtained via noninvasive X-ray fluorescence
imaging of their canvases. This recently developed imaging
technique measures the concentrations of various chemical
elements at each two-dimensional spatial location across the
canvas. These concentrations in turn result from pigments
present both in the surface painting and in the hidden
painting beneath. These X-ray fluorescence images provide
the best available data from which to noninvasively study a
hidden painting. However, they are typically marred by
artifacts of the imaging process, features of the surface
painting, and areas of information loss. Repairing and
restoring these images thus consists of three stages: (1)
repairing acquisition artifacts in the dataset, (2) removal
of features in the images that result from the surface
painting rather than the hidden painting, and (3)
identification and repair of areas of information loss. We
describe methods we have developed to address each of these
stages: a total-variation minimization approach to artifact
correction, a novel method for underdetermined blind source
separation with multimodal side information to address
surface feature removal, and two application-specific new
methods for automatically identifying particularly thick or
X-ray absorbent surface features in the painting. Finally,
we demonstrate the results of our methods on a hidden
painting by the artist Vincent van Gogh. © 2012 Elsevier
B.V.},
Doi = {10.1016/j.sigpro.2012.09.027},
Key = {fds287203}
}

@article{fds303542,
Author = {Lipman, Y and Puente, J and Daubechies, I},
Title = {Conformal Wasserstein distance: II. Computational aspects
and extensions},
Journal = {Mathematics of Computation},
Volume = {82},
Number = {281},
Pages = {331-381},
Publisher = {American Mathematical Society (AMS)},
Year = {2013},
Month = {January},
url = {http://arxiv.org/abs/1103.4681v2},
Abstract = {This paper is a companion paper to [Yaron Lipman and Ingrid
Daubechies, Conformal Wasserstein distances: Comparing
surfaces in polynomial time, Adv. in Math. (ELS), 227
(2011), no. 3, 1047-1077, (2011)]. We provide numerical
procedures and algorithms for computing the alignment of and
distance between two disk-type surfaces. We provide a
convergence analysis of the discrete approximation to the
arising mass-transportation problems. We furthermore
generalize the framework to support sphere-type surfaces,
and prove a result connecting this distance to local
geodesic distortion. Finally, we perform numerical
experiments on several surface datasets and compare them to
state-of-the-art methods. © 2012 American Mathematical
Society.},
Doi = {10.1090/S0025-5718-2012-02569-5},
Key = {fds303542}
}

@article{fds320874,
Author = {Puente, J and Boyer, DM and Gladman, JT and Daubechies,
IC},
Title = {Automated approaches to geometric morphometrics.},
Journal = {American Journal of Physical Anthropology},
Volume = {150},
Pages = {226-226},
Publisher = {WILEY-BLACKWELL},
Year = {2013},
Month = {January},
Key = {fds320874}
}

@article{fds287106,
Author = {Al-Aifari, R and Daubechies, I and Lipman, Y},
Title = {Continuous Procrustes distance between two
surfaces},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {66},
Number = {6},
Pages = {934-964},
Year = {2013},
ISSN = {0010-3640},
url = {http://dx.doi.org/10.1002/cpa.21444},
Abstract = {The Procrustes distance is used to quantify the similarity
or dissimilarity of (three-dimensional) shapes and
extensively used in biological morphometrics. Typically each
(normalized) shape is represented by N landmark points,
chosen to be homologous, as far as possible, and the
Procrustes distance is then computed as $\inf_{R}\sum_{j=1}^N \|Rx_j-x'_j\|^2$, where the minimization is over all
euclidean transformations, and the correspondences $x_j \leftrightarrow x'_j$ are picked in an optimal way. The
discrete Procrustes distance has the drawback that each
shape is represented by only a finite number of points,
which may not capture all the geometric aspects of interest;
a need has been expressed for alternatives that are still
easy to compute. We propose in this paper the concept of
continuous Procrustes distance and prove that it provides a
true metric for two-dimensional surfaces embedded in three
dimensions. We also propose an efficient algorithm to
calculate approximations to this new distance. © 2013 Wiley
Periodicals, Inc.},
Doi = {10.1002/cpa.21444},
Key = {fds287106}
}

@article{fds287202,
Author = {Roussos, E and Roberts, S and Daubechies, I},
Title = {Variational Bayesian learning of sparse representations and
its application in functional neuroimaging},
Journal = {Lecture Notes in Computer Science (Including Subseries
Lecture Notes in Artificial Intelligence and Lecture Notes
in Bioinformatics)},
Volume = {7263 LNAI},
Pages = {218-225},
Publisher = {Springer Berlin Heidelberg},
Year = {2012},
Month = {November},
ISSN = {0302-9743},
url = {http://dx.doi.org/10.1007/978-3-642-34713-9_28},
Abstract = {Recent theoretical and experimental work in imaging
neuroscience reveals that activations inferred from
functional MRI data have sparse structure. We view sparse
representation as a problem in Bayesian inference, following
a machine learning approach, and construct a structured
sparsity-inducing priors. The construction allows for
automatic complexity control and regularization as well as
denoising. Experimental results with benchmark datasets show
that the proposed algorithm outperforms standard tools for
model-free decompositions such as independent component
Doi = {10.1007/978-3-642-34713-9_28},
Key = {fds287202}
}

@article{fds287201,
Author = {Cohen, A and Daubechies, I and DeVore, R and Kerkyacharian, G and Picard, D},
Title = {Capturing Ridge Functions in High Dimensions from Point
Queries},
Journal = {Constructive Approximation},
Volume = {35},
Number = {2},
Pages = {225-243},
Publisher = {Springer Nature},
Year = {2012},
Month = {April},
ISSN = {0176-4276},
url = {http://dx.doi.org/10.1007/s00365-011-9147-6},
Abstract = {Constructing a good approximation to a function of many
variables suffers from the "curse of dimensionality".
Namely, functions on ℝ N with smoothness of order s can in
general be captured with accuracy at most O(n -s/N) using
linear spaces or nonlinear manifolds of dimension n. If N is
large and s is not, then n has to be chosen inordinately
large for good accuracy. The large value of N often
precludes reasonable numerical procedures. On the other
hand, there is the common belief that real world problems in
high dimensions have as their solution, functions which are
more amenable to numerical recovery. This has led to the
introduction of models for these functions that do not
depend on smoothness alone but also involve some form of
variable reduction. In these models it is assumed that,
although the function depends on N variables, only a small
number of them are significant. Another variant of this
principle is that the function lives on a low dimensional
manifold. Since the dominant variables (respectively the
manifold) are unknown, this leads to new problems of how to
organize point queries to capture such functions. The
present paper studies where to query the values of a ridge
function f(x)=g(a · x) when both a∈ℝ N and g ∈ C[0,1]
are unknown. We establish estimates on how well f can be
approximated using these point queries under the assumptions
that g ∈ C s[0,1]. We also study the role of sparsity or
compressibility of a in such query problems. © 2011
Doi = {10.1007/s00365-011-9147-6},
Key = {fds287201}
}

@article{fds215104,
Author = {I. Daubechies},
Title = {Developing Mathematical Tools to Investigate
Art},
Booktitle = {Bridges 2012 Proceedings},
Publisher = {Jacobs Publishing},
Editor = {Robert Bosch and Douglas McKenna and Reza Sarhangi},
Year = {2012},
Abstract = {This paper tells the history of a project investigating
authenticity and forgery in Van Gogh paintings using
mathematical tools based on wavelet transformations.},
Key = {fds215104}
}

@article{fds287195,
Author = {Platiša, L and Cornells, B and Ružić, T and Pižurica, A and Dooms,
A and Martens, M and De Mey and M and Daubechies, I},
Title = {Spatiogram features to characterize pearls in
paintings},
Journal = {Proceedings International Conference on Image Processing,
Icip},
Pages = {801-804},
Publisher = {IEEE},
Year = {2011},
Month = {December},
ISSN = {1522-4880},
url = {http://dx.doi.org/10.1109/ICIP.2011.6116677},
Abstract = {Objective characterization of jewels in paintings,
especially pearls, has been a long lasting challenge for art
historians. The way an artist painted pearls reflects his
ability to observing nature and his knowledge of
contemporary optical theory. Moreover, the painterly
execution may also be considered as an individual
characteristic useful in distinguishing hands. In this work,
we propose a set of image analysis techniques to analyze and
measure spatial characteristics of the digital images of
pearls, all relying on the so called spatiogram image
representation. Our experimental results demonstrate good
correlation between the new metrics and the visually
observed image features, and also capture the degree of
realism of the visual appearance in the painting. In that
sense, these results set the basis in creating a practical
tool for art historical attribution and give strong
motivation for further investigations in this direction. ©
2011 IEEE.},
Doi = {10.1109/ICIP.2011.6116677},
Key = {fds287195}
}

@article{fds287197,
Author = {Anitha, A and Brasoveanu, A and Duarte, MF and Hughes, SM and Daubechies, I and Dik, J and Janssens, K and Alfeld,
M},
Title = {Virtual underpainting reconstruction from X-ray fluorescence
imaging data},
Journal = {European Signal Processing Conference},
Pages = {1239-1243},
Year = {2011},
Month = {December},
ISSN = {2219-5491},
Abstract = {This paper describes our work on the problem of
reconstructing the original visual appearance of
underpaintings (paintings that have been painted over and
are now covered by a new surface painting) from noninvasive
X-ray fluorescence imaging data of their canvases. This
recently-developed imaging technique yields data revealing
the concentrations of various chemical elements at each
spatial location across the canvas. These concentrations in
turn result from pigments present in both the surface
painting and the underpainting beneath. Reconstructing a
visual image of the underpainting from this data involves
repairing acquisition artifacts in the dataset,
underdetermined source separation into surface and
underpainting features, identification and inpainting of
areas of information loss, and finally estimation of the
original paint colors from the chemical element data. We
will describe methods we have developed to address each of
these stages of underpainting recovery and show results on
Key = {fds287197}
}

@article{fds287196,
Author = {Simons, FJ and Loris, I and Brevdo, E and Daubechies,
IC},
Title = {Wavelets and wavelet-like transforms on the sphere and their
application to geophysical data inversion},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {8138},
Publisher = {SPIE},
Year = {2011},
Month = {November},
ISSN = {0277-786X},
url = {http://dx.doi.org/10.1117/12.892285},
Abstract = {Many flexible parameterizations exist to represent data on
the sphere. In addition to the venerable spherical
harmonics, we have the Slepian basis, harmonic splines,
wavelets and wavelet-like Slepian frames. In this paper we
focus on the latter two: spherical wavelets developed for
geophysical applications on the cubed sphere, and the
Slepian "tree", a new construction that combines a quadratic
concentration measure with wavelet-like multiresolution. We
discuss the basic features of these mathematical tools, and
illustrate their applicability in parameterizing large-scale
Society of Photo-Optical Instrumentation Engineers
(SPIE).},
Doi = {10.1117/12.892285},
Key = {fds287196}
}

@article{fds287210,
Author = {Simons, FJ and Loris, I and Nolet, G and Daubechies, IC and Voronin, S and Judd, JS and Vetter, PA and Charléty, J and Vonesch,
C},
Title = {Solving or resolving global tomographic models with
spherical wavelets, and the scale and sparsity of seismic
heterogeneity},
Journal = {Geophysical Journal International},
Volume = {187},
Number = {2},
Pages = {969-988},
Year = {2011},
Month = {November},
ISSN = {0956-540X},
url = {http://dx.doi.org/10.1111/j.1365-246X.2011.05190.x},
Abstract = {We propose a class of spherical wavelet bases for the
analysis of geophysical models and for the tomographic
inversion of global seismic data. Its multiresolution
character allows for modelling with an effective spatial
resolution that varies with position within the Earth. Our
procedure is numerically efficient and can be implemented
with parallel computing. We discuss two possible types of
discrete wavelet transforms in the angular dimension of the
cubed sphere. We describe benefits and drawbacks of these
constructions and apply them to analyse the information in
two published seismic wave speed models of the mantle, using
the statistics of wavelet coefficients across scales. The
localization and sparsity properties of wavelet bases allow
finding a sparse solution to inverse problems by iterative
minimization of a combination of the ℓ2 norm of the data
residuals and the ℓ1 norm of the model wavelet
coefficients. By validation with realistic synthetic
experiments we illustrate the likely gains from our new
approach in future inversions of finite-frequency seismic
data. © 2011 The Authors Geophysical Journal International
Doi = {10.1111/j.1365-246X.2011.05190.x},
Key = {fds287210}
}

@article{fds287211,
Author = {Boyer, DM and Lipman, Y and St Clair and E and Puente, J and Patel, BA and Funkhouser, T and Jernvall, J and Daubechies, I},
Title = {Algorithms to automatically quantify the geometric
similarity of anatomical surfaces.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {108},
Number = {45},
Pages = {18221-18226},
Year = {2011},
Month = {November},
ISSN = {1091-6490},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22025685},
Abstract = {We describe approaches for distances between pairs of
two-dimensional surfaces (embedded in three-dimensional
space) that use local structures and global information
contained in interstructure geometric relationships. We
present algorithms to automatically determine these
distances as well as geometric correspondences. This
approach is motivated by the aspiration of students of
natural science to understand the continuity of form that
unites the diversity of life. At present, scientists using
physical traits to study evolutionary relationships among
living and extinct animals analyze data extracted from
carefully defined anatomical correspondence points
(landmarks). Identifying and recording these landmarks is
time consuming and can be done accurately only by trained
morphologists. This necessity renders these studies
inaccessible to nonmorphologists and causes phenomics to lag
behind genomics in elucidating evolutionary patterns. Unlike
other algorithms presented for morphological
correspondences, our approach does not require any
preliminary marking of special features or landmarks by the
user. It also differs from other seminal work in
computational geometry in that our algorithms are polynomial
in nature and thus faster, making pairwise comparisons
feasible for significantly larger numbers of digitized
surfaces. We illustrate our approach using three datasets
representing teeth and different bones of primates and
humans, and show that it leads to highly accurate
results.},
Doi = {10.1073/pnas.1112822108},
Key = {fds287211}
}

@article{fds287194,
Author = {Ružić, T and Cornelis, B and Platiša, L and Pižurica, A and Dooms,
A and Philips, W and Martens, M and De Mey and M and Daubechies,
I},
Title = {Virtual restoration of the Ghent altarpiece using crack
detection and inpainting},
Journal = {Lecture Notes in Computer Science (Including Subseries
Lecture Notes in Artificial Intelligence and Lecture Notes
in Bioinformatics)},
Volume = {6915 LNCS},
Pages = {417-428},
Publisher = {Springer Berlin Heidelberg},
Year = {2011},
Month = {September},
ISSN = {0302-9743},
url = {http://dx.doi.org/10.1007/978-3-642-23687-7_38},
Abstract = {In this paper, we present a new method for virtual
restoration of digitized paintings, with the special focus
on the Ghent Altarpiece (1432), one of Belgium's greatest
masterpieces. The goal of the work is to remove cracks from
the digitized painting thereby approximating how the
painting looked like before ageing for nearly 600 years and
aiding art historical and palaeographical analysis. For
crack detection, we employ a multiscale morphological
approach, which can cope with greatly varying thickness of
the cracks as well as with their varying intensities (from
dark to the light ones). Due to the content of the painting
(with extremely many fine details) and complex type of
cracks (including inconsistent whitish clouds around them),
the available inpainting methods do not provide satisfactory
results on many parts of the painting. We show that
patch-based methods outperform pixel-based ones, but leaving
still much room for improvements in this application. We
propose a new method for candidate patch selection, which
can be combined with different patch-based inpainting
methods to improve their performance in crack removal. The
results demonstrate improved performance, with less
artefacts and better preserved fine details. © 2011
Springer-Verlag.},
Doi = {10.1007/978-3-642-23687-7_38},
Key = {fds287194}
}

@article{fds287207,
Author = {Wolff, J and Martens, M and Jafarpour, S and Daubechies, I and Calderbank, R},
Title = {Uncovering elements of style},
Journal = {2015 Ieee International Conference on Acoustics, Speech, and
Signal Processing (Icassp)},
Pages = {1017-1020},
Publisher = {IEEE},
Year = {2011},
Month = {August},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2011.5946579},
Abstract = {This paper relates the style of 16th century Flemish
paintings by Goossen van der Weyden (GvdW) to the style of
preliminary sketches or underpaintings made prior to
executing the painting. Van der Weyden made underpaintings
in markedly different styles for reasons as yet not
understood by art historians. The analysis presented here
starts from a classification of the underpaintings into four
distinct styles by experts in art history. Analysis of the
painted surfaces by a combination of wavelet analysis,
hidden Markov trees and boosting algorithms can distinguish
the four underpainting styles with greater than 90%
cross-validation accuracy. On a subsequent blind test this
classifier provided insight into the hypothesis by art
historians that different patches of the finished painting
were executed by different hands. © 2011
IEEE.},
Doi = {10.1109/ICASSP.2011.5946579},
Key = {fds287207}
}

@article{fds287208,
Author = {Lipman, Y and Daubechies, I},
Title = {Conformal Wasserstein distances: Comparing surfaces in
polynomial time},
Volume = {227},
Number = {3},
Pages = {1047-1077},
Publisher = {Elsevier BV},
Year = {2011},
Month = {June},
ISSN = {0001-8708},
url = {http://dx.doi.org/10.1016/j.aim.2011.01.020},
Abstract = {We present a constructive approach to surface comparison
realizable by a polynomial-time algorithm. We determine the
"similarity" of two given surfaces by solving a
mass-transportation problem between their conformal
densities. This mass transportation problem differs from the
standard case in that we require the solution to be
invariant under global Möbius transformations. We present
in detail the case where the surfaces to compare are
disk-like; we also sketch how the approach can be
generalized to other types of surfaces. © 2011 Elsevier
Inc.},
Doi = {10.1016/j.aim.2011.01.020},
Key = {fds287208}
}

@article{fds287198,
Author = {Bunn, JM and Boyer, DM and Lipman, Y and St Clair and EM and Jernvall, J and Daubechies, I},
Title = {Comparing Dirichlet normal surface energy of tooth crowns, a
new technique of molar shape quantification for dietary
inference, with previous methods in isolation and in
combination.},
Journal = {American Journal of Physical Anthropology},
Volume = {145},
Number = {2},
Pages = {247-261},
Year = {2011},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21469070},
Abstract = {Inferred dietary preference is a major component of
paleoecologies of extinct primates. Molar occlusal shape
correlates with diet in living mammals, so teeth are a
potentially useful structure from which to reconstruct diet
in extinct taxa. We assess the efficacy of Dirichlet normal
energy (DNE) calculated for molar tooth surfaces for
reflecting diet. We evaluate DNE, which uses changes in
normal vectors to characterize curvature, by directly
comparing this metric to metrics previously used in dietary
inference. We also test whether combining methods improves
diet reconstructions. The study sample consisted of 146
lower (mandibular) second molars belonging to 24 euarchontan
taxa. Five shape quantification metrics were calculated on
each molar: DNE, shearing quotient, shearing ratio, relief
index, and orientation patch count rotated (OPCR).
Statistical analyses were completed for each variable to
assess effects of taxon and diet. Discriminant function
analysis was used to assess ability of combinations of
variables to predict diet. Values differ significantly by
diets for all variables, although shearing ratios and OPCR
do not distinguish statistically between insectivores and
folivores or omnivores and frugivores. Combined analyses
were much more effective at predicting diet than any metric
alone. Alone, relief index and DNE were most effective at
predicting diet. OPCR was the least effective alone but is
still valuable as the only quantitative measure of surface
complexity. Of all methods considered, DNE was the least
methodologically sensitive, and its effectiveness suggests
it will be a valuable tool for dietary reconstruction.},
Doi = {10.1002/ajpa.21489},
Key = {fds287198}
}

@article{fds287103,
Author = {Dooms, A and Daubechies, I},
Title = {Wavelets},
Pages = {135-154},
Publisher = {Wiley-VCH Verlag GmbH & Co. KGaA},
Year = {2011},
Month = {April},
url = {http://dx.doi.org/10.1002/9783527635245.ch7},
Doi = {10.1002/9783527635245.ch7},
Key = {fds287103}
}

@article{fds287199,
Author = {Wu, HT and Flandrin, P and Daubechies, I},
Title = {One or two frequencies? the synchrosqueezing
Volume = {3},
Number = {1-2},
Pages = {29-39},
Publisher = {World Scientific Pub Co Pte Lt},
Year = {2011},
Month = {April},
ISSN = {1793-5369},
url = {http://dx.doi.org/10.1142/S179353691100074X},
Abstract = {The synchrosqueezed transform was proposed recently in
[Daubechies et al. (2009)] as an alternative to the
empirical mode decomposition (EMD) [Huang et al. (1998)], to
decompose composite signals into a sum of "modes" that each
have well-defined instantaneous frequencies. This paper
presents, for synchrosqueezing, a study similar to that in
[Rilling and Flandrin (2008)] for EMD, of how two signals
with close frequencies are recognized and represented as
such. © 2011 World Scientific Publishing
Company.},
Doi = {10.1142/S179353691100074X},
Key = {fds287199}
}

@article{fds303540,
Author = {Daubechies, I and Lu, J and Wu, H-T},
Title = {Synchrosqueezed wavelet transforms: An empirical mode
decomposition-like tool},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {30},
Number = {2},
Pages = {243-261},
Publisher = {Elsevier BV},
Year = {2011},
Month = {March},
url = {http://arxiv.org/abs/0912.2437v1},
Abstract = {The EMD algorithm, first proposed in [11], made more robust
as well as more versatile in [12], is a technique that aims
to decompose into their building blocks functions that are
the superposition of a (reasonably) small number of
components, well separated in the time-frequency plane, each
of which can be viewed as approximately harmonic locally,
with slowly varying amplitudes and frequencies. The EMD has
already shown its usefulness in a wide range of applications
including meteorology, structural stability analysis,
medical studies -- see, e.g. [13]. On the other hand, the
EMD algorithm contains heuristic and ad-hoc elements that
make it hard to analyze mathematically. In this paper we
describe a method that captures the flavor and philosophy of
the EMD approach, albeit using a different approach in
constructing the components. We introduce a precise
mathematical definition for a class of functions that can be
viewed as a superposition of a reasonably small number of
approximately harmonic components, and we prove that our
method does indeed succeed in decomposing arbitrary
functions in this class. We provide several examples, for
simulated as well as real data.},
Doi = {10.1016/j.acha.2010.08.002},
Key = {fds303540}
}

@article{fds201618,
Author = {B. Cornelis and A. Dooms and I. Daubechies and P.
Schelkens},
Title = {Report on Digital Image Processing for Art
Historians},
Journal = {Sampling Theory and Applications, SampTA '09, Marseille
France, May 18-22, 2009},
Year = {2011},
Key = {fds201618}
}

@article{fds287105,
Author = {Daubechies, I},
Title = {The work of Yves Meyer},
Journal = {Proceedings of the International Congress of Mathematicians
2010, Icm 2010},
Pages = {114-124},
Year = {2010},
Month = {December},
Abstract = {Yves Meyer has made numerous contributions to mathematics,
several of which will be reviewed here, in particular in
number theory, harmonic analysis and partial differential
equations. His work in harmonic analysis led him naturally
to take an interest in wavelets, when they emerged in the
early 1980s; his synthesis of the advanced theoretical
results in singular integral operator theory, established by
himself and others, and of the requirements imposed by
practical applications, led to enormous progress for wavelet
theory and its applications. Wavelets and wavelet packets
are now standard, extremely useful tools in many
disciplines; their success is due in large measure to the
vision, the insight and the enthusiasm of Yves
Meyer.},
Key = {fds287105}
}

@article{fds287193,
Author = {Daubechies, I and Güntürk, CS and Wang, Y and Yilmaz,
O},
Title = {The golden ratio encoder},
Journal = {Ieee Transactions on Information Theory},
Volume = {56},
Number = {10},
Pages = {5097-5110},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2010},
Month = {October},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2010.2059750},
Abstract = {This paper proposes a novel Nyquist-rate analog-to-digital
(A/D) conversion algorithm which achieves exponential
accuracy in the bit-rate despite using imperfect components.
The proposed algorithm is based on a robust implementation
of a beta-encoder with β = φ =(1+ √5)/2, the golden
ratio. It was previously shown that beta-encoders can be
implemented in such a way that their exponential accuracy is
robust against threshold offsets in the quantizer element.
This paper extends this result by allowing for imperfect
analog multipliers with imprecise gain values as well.
Furthermore, a formal computational model for algorithmic
encoders and a general test bed for evaluating their
robustness is proposed. © 2010 IEEE.},
Doi = {10.1109/TIT.2010.2059750},
Key = {fds287193}
}

@article{fds287190,
Author = {Lipman, Y and Chen, X and Daubechies, I and Funkhouser,
T},
Title = {Symmetry factored embedding and distance},
Journal = {Acm Siggraph 2010 Papers, Siggraph 2010},
Volume = {29},
Number = {4},
Pages = {1-1},
Publisher = {Association for Computing Machinery (ACM)},
Year = {2010},
Month = {July},
ISSN = {0730-0301},
url = {http://dx.doi.org/10.1145/1778765.1778840},
Abstract = {© 2010 ACM. We introduce the Symmetry Factored Embedding
(SFE) and the Symmetry Factored Distance (SFD) as new tools
to analyze and represent symmetries in a point set. The SFE
provides new coordinates in which symmetry is "factored
out," and the SFD is the Euclidean distance in that space.
These constructions characterize the space of symmetric
correspondences between points - i.e., orbits. A key
observation is that a set of points in the same orbit
appears as a clique in a correspondence graph induced by
pairwise similarities. As a result, the problem of finding
approximate and partial symmetries in a point set reduces to
the problem of measuring connectedness in the correspondence
graph, a well-studied problem for which spectral methods
provide a robust solution. We provide methods for computing
the SFE and SFD for extrinsic global symmetries and then
extend them to consider partial extrinsic and intrinsic
cases. During experiments with difficult examples, we find
that the proposed methods can characterize symmetries in
inputs with noise, missing data, non-rigid deformations, and
complex symmetries, without a priori knowledge of the
symmetry group. As such, we believe that it provides a
useful tool for automatic shape analysis in applications
such as segmentation and stationary point
detection.},
Doi = {10.1145/1778765.1778840},
Key = {fds287190}
}

@article{fds287093,
Author = {Daubechies, I},
Title = {Wavelets and applications},
Pages = {848-862},
Year = {2010},
Month = {July},
Key = {fds287093}
}

@article{fds287192,
Author = {Loris, I and Douma, H and Nolet, G and Daubechies, I and Regone,
C},
Title = {Nonlinear regularization techniques for seismic
tomography},
Journal = {Journal of Computational Physics},
Volume = {229},
Number = {3},
Pages = {890-905},
Publisher = {Elsevier BV},
Year = {2010},
Month = {February},
ISSN = {0021-9991},
url = {http://dx.doi.org/10.1016/j.jcp.2009.10.020},
Abstract = {The effects of several nonlinear regularization techniques
are discussed in the framework of 3D seismic tomography.
Traditional, linear, ℓ2 penalties are compared to
so-called sparsity promoting ℓ1 and ℓ0 penalties, and a
total variation penalty. Which of these algorithms is judged
optimal depends on the specific requirements of the
scientific experiment. If the correct reproduction of model
amplitudes is important, classical damping towards a smooth
model using an ℓ2 norm works almost as well as minimizing
the total variation but is much more efficient. If gradients
(edges of anomalies) should be resolved with a minimum of
distortion, we prefer ℓ1 damping of Daubechies-4 wavelet
noiseless reconstruction, contrary to simple ℓ2
minimization ('Tikhonov regularization') which should be
avoided. In some of our examples, the ℓ0 method produced
notable artifacts. In addition we show how nonlinear ℓ1
methods for finding sparse models can be competitive in
speed with the widely used ℓ2 methods, certainly under
noisy conditions, so that there is no need to shun ℓ1
penalizations. © 2009 Elsevier Inc. All rights
reserved.},
Doi = {10.1016/j.jcp.2009.10.020},
Key = {fds287192}
}

@article{fds287189,
Author = {Daubechies, I and Devore, R and Fornasier, M and Güntürk,
CS},
Title = {Iteratively reweighted least squares minimization for sparse
recovery},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {63},
Number = {1},
Pages = {1-38},
Publisher = {WILEY},
Year = {2010},
Month = {January},
ISSN = {0010-3640},
url = {http://dx.doi.org/10.1002/cpa.20303},
Abstract = {Under certain conditions (known as the restricted isometry
property, or RIP) on the m × N matrix Φ (wherem < N),
vectors x ∈ R{double-struck}N that are sparse (i.e., have
most of their entries equal to 0) can be recovered exactly
from y:= Φx even though Φ-1(y). is typically an
(N-m)-dimensional hyperplane; in addition, x is then equal
to the element in Φ-1(y) of minimal l1-norm. This minimal
element can be identified via linear programming algorithms.
We study an alternative method of determining x, as the
limit of an iteratively reweighted least squares (IRLS)
algorithm. The main step of this IRLS finds, for a given
weight vector w, the element in Φ-1(y) with smallest
l2.(w)-norm. If x(n) is the solution at iteration step n,
then the new weight w(n)i/ is defined by for a decreasing
sequence of adaptively defined εn; this updated weight is
then used to obtain x(n+1)/ and the process is repeated. We
prove that when ̂ satisfies the RIP conditions, the
sequence x(n) converges for all y, regardless of whether
Φ-1(y), contains a sparse vector. If there is a sparse
vector in Φ-1(y), then the limit is this sparse vector, and
when x.(n) is sufficiently close to the limit, the remaining
steps of the algorithm converge exponentially fast (linear
convergence in the terminology of numerical optimization).
The same algorithm with the "heavier" weight, can recover
sparse solutions as well; more importantly, we show its
local convergence is superlinear and approaches a quadratic
rate for approaching 0. © 2009 Wiley Periodicals,
Inc.},
Doi = {10.1002/cpa.20303},
Key = {fds287189}
}

@article{fds287191,
Author = {Kobiler, O and Lipman, Y and Therkelsen, K and Daubechies, I and Enquist, LW},
Title = {Herpesviruses carrying a Brainbow cassette reveal
replication and expression of limited numbers of incoming
genomes.},
Journal = {Nature Communications},
Volume = {1},
Pages = {146},
Year = {2010},
Month = {January},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21266996},
Abstract = {Whether all the infectious herpesvirus particles entering a
cell are able to replicate and/or express their genomes is
not known. Here, we developed a general method to determine
the number of viral genomes expressed in an infected cell.
We constructed and analysed fluorophore expression from a
recombinant pseudorabies virus (PRV263) carrying a Brainbow
cassette (Cre-conditional expression of different
fluorophores). Using three isogenic strains derived from
PRV263, each expressing a single fluorophore, we analysed
the colour composition of cells infected with these three
viruses at different multiplicities. We estimate that fewer
than seven incoming genomes are expressed per cell. In
addition, those templates that are expressed are the genomes
selected for replication and packaging into virions. This
finite limit on the number of viral genomes that can be
expressed is an intrinsic property of the infected cell and
may be influenced by viral and cellular factors.},
Doi = {10.1038/ncomms1145},
Key = {fds287191}
}

@article{fds287185,
Author = {Jafarpour, S and Polatkan, G and Brevdo, E and Hughes, S and Brasoveanu,
A and Daubechies, I},
Title = {Stylistic analysis of paintings using wavelets and machine
learning},
Journal = {European Signal Processing Conference},
Pages = {1220-1224},
Year = {2009},
Month = {December},
ISSN = {2219-5491},
Abstract = {Wavelet transforms and machine learning tools can be used to
assist art experts in the stylistic analysis of paintings. A
dual-tree complex wavelet transform, Hidden Markov Tree
modeling and Random Forest classifiers are used here for a
stylistic analysis of Vincent van Gogh's paintings with
results on two stylometry challenges that concern "dating,
resp. extracting distinguishing features". © EURASIP,
2009.},
Key = {fds287185}
}

@article{fds287188,
Author = {Brodie, J and Daubechies, I and De Mol and C and Giannone, D and Loris,
I},
Title = {Sparse and stable Markowitz portfolios.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {106},
Number = {30},
Pages = {12267-12272},
Year = {2009},
Month = {July},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19617537},
Abstract = {We consider the problem of portfolio selection within the
classical Markowitz mean-variance framework, reformulated as
a constrained least-squares regression problem. We propose
to add to the objective function a penalty proportional to
the sum of the absolute values of the portfolio weights.
This penalty regularizes (stabilizes) the optimization
problem, encourages sparse portfolios (i.e., portfolios with
only few active positions), and allows accounting for
transaction costs. Our approach recovers as special cases
the no-short-positions portfolios, but does allow for short
positions in limited number. We implement this methodology
on two benchmark data sets constructed by Fama and French.
Using only a modest amount of training data, we construct
portfolios whose out-of-sample performance, as measured by
Sharpe ratio, is consistently and significantly better than
that of the naïve evenly weighted portfolio.},
Doi = {10.1073/pnas.0904287106},
Key = {fds287188}
}

@article{fds287187,
Author = {Daubechies, I and Roussos, E and Takerkart, S and Benharrosh, M and Golden, C and D'Ardenne, K and Richter, W and Cohen, JD and Haxby,
J},
Title = {Independent component analysis for brain fMRI does not
select for independence.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {106},
Number = {26},
Pages = {10415-10422},
Year = {2009},
Month = {June},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19556548},
Abstract = {InfoMax and FastICA are the independent component analysis
algorithms most used and apparently most effective for brain
fMRI. We show that this is linked to their ability to handle
effectively sparse components rather than independent
components as such. The mathematical design of better
analysis tools for brain fMRI should thus emphasize other
mathematical characteristics than independence.},
Doi = {10.1073/pnas.0903525106},
Key = {fds287187}
}

@article{fds287090,
Author = {Daubechies, I},
Title = {The wavelet transform, time-frequency localization and
signal analysis},
Pages = {442-486},
Year = {2009},
Month = {January},
Two different procedures are studied by which a rrequency
analysis of a time-dependenl signal can be effected, locally
in lime. The lirst procedure is the short-time or windowed
Fourier transform, the second is the "wavelet transform," in
which high frequency components are sludied wilh sharper
time resolution than low frequency components. The
similarities and the differences between these two methods
are discussed. For both scbemes a detailed study is made of
Ibe reconslruetion method and ils stability, as a function
of the chosen time-frequency density. Finally the notion of
"time-frequency localization" is made precise, within this
framework, by two localization theorems.},
Key = {fds287090}
}

@article{fds287091,
Author = {Daubechies, I and Grossmann, A and Meyer, Y},
Title = {Painless nonorthogonal expansions},
Pages = {372-384},
Year = {2009},
Month = {January},
In a Hilbert space {Hilbert space}, discrete families of
vectors {hj} with the property that f = ΣJ <hJ|f> hJ for
every f in {Hilbert space} are considered. This expansion
formula is obviously true if the family is an orthonorma1
basis of {Hilbert space}, but also can hold in situations
where the hj are not mutually orthogonal and are
"overcomplete." The two classes of examples studied here are
(i) appropriate sets of Weyl-Heisenberg coherent states,
based on certain (non-Gaussian) fiducial vectors, and (ii)
analogous families of affine coherent states. It is
believed, that such "quasiorthogonal expansions" will be a
useful tool in many areas of theoretical physics and applied
mathematics.},
Key = {fds287091}
}

@article{fds287092,
Author = {Daubechies, I},
Title = {Foreword},
Pages = {xv-xvi},
Year = {2009},
Month = {January},
ISBN = {0691114536},
Key = {fds287092}
}

@article{fds287186,
Author = {Polatkan, G and Jafarpour, S and Brasoveanu, A and Hughes, S and Daubechies, I},
Title = {Detection of forgery in paintings using supervised
learning},
Journal = {Proceedings International Conference on Image Processing,
Icip},
Pages = {2921-2924},
Publisher = {IEEE},
Year = {2009},
Month = {January},
ISSN = {1522-4880},
url = {http://dx.doi.org/10.1109/ICIP.2009.5413338},
Abstract = {This paper examines whether machine learning and image
analysis tools can be used to assist art experts in the
authentication of unknown or disputed paintings. Recent work
on this topic [1] has presented some promising initial
results. Our reexamination of some of these recently
successful experiments shows that variations in image
clarity in the experimental datasets were correlated with
authenticity, and may have acted as a confounding factor,
artificially improving the results. To determine the extent
of this factor's influence on previous results, we provide a
new "ground truth" data set in which originals and copies
are known and image acquisition conditions are uniform.
Multiple previously-successful methods are found ineffective
on this new confounding-factor-free dataset, but we
demonstrate that supervised machine learning on features
derived from Hidden-Markov-Tree-modeling of the paintings'
wavelet coefficients has the potential to distinguish copies
from originals in the new dataset. ©2009
IEEE.},
Doi = {10.1109/ICIP.2009.5413338},
Key = {fds287186}
}

@article{fds287183,
Author = {Daubechies, I and Fornasier, M and Loris, I},
Title = {Accelerated projected gradient method for linear inverse
problems with sparsity constraints},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {14},
Number = {5-6},
Pages = {764-792},
Publisher = {Springer Nature},
Year = {2008},
Month = {December},
ISSN = {1069-5869},
url = {http://dx.doi.org/10.1007/s00041-008-9039-8},
Abstract = {Regularization of ill-posed linear inverse problems via ℓ1
penalization has been proposed for cases where the solution
is known to be (almost) sparse. One way to obtain the
minimizer of such an ℓ1 penalized functional is via an
iterative soft-thresholding algorithm. We propose an
alternative implementation to ℓ1-constraints, using a
gradient method, with projection on ℓ1-balls. The
corresponding algorithm uses again iterative
soft-thresholding, now with a variable thresholding
parameter. We also propose accelerated versions of this
iterative method, using ingredients of the (linear) steepest
descent method. We prove convergence in norm for one of
these projected gradient methods, without and with
Doi = {10.1007/s00041-008-9039-8},
Key = {fds287183}
}

@article{fds287182,
Author = {Daubechies, I and DeVore, R and Fornasier, M and Güntürk,
S},
Title = {Iteratively Re-weighted Least Squares minimization: Proof of
faster than linear rate for sparse recovery},
Journal = {Ciss 2008, the 42nd Annual Conference on Information
Sciences and Systems},
Pages = {26-29},
Publisher = {IEEE},
Year = {2008},
Month = {September},
url = {http://dx.doi.org/10.1109/CISS.2008.4558489},
Abstract = {Given an m × N matrix Φ, with m < N, the system of
equations Φx = y is typically underdetermined and has
infinitely many solutions. Various forms of optimization can
extract a "best" solution. One of the oldest is to select
the one with minimal l2 norm. It has been shown that in many
applications a better choice is the minimal l1 norm
solution. This is the case in Compressive Sensing, when
sparse solutions are sought. The minimal l1 norm solution
can be found by using linear programming; an alternative
method is Iterative Re-weighted Least Squares (IRLS), which
in some cases is numerically faster. The main step of IRLS
finds, for a given weight w, the solution with smallest
l2(w) norm; this weight is updated at every iteration step:
if x(n) is the solution at step n, then w(n) is defined by
wi(n):= 1/|xi(n)|, i = 1,..., N. We give a specific recipe
for updating weights that avoids technical shortcomings in
other approaches, and for which we can prove convergence
under certain conditions on the matrix Φ known as the
Restricted Isometry Property. We also show that if there is
a sparse solution, then the limit of the proposed algorithm
is that sparse solution. It is also shown that whenever the
solution at a given iteration is sufficiently close to the
limit, then the remaining steps of the algorithm converge
exponentially fast. In the standard version of the
algorithm, designed to emulate l1-minimization, the
exponenital rate is linear; in adapted versions aimed at
1T-minimization with T <1, we prove faster than linear rate.
Doi = {10.1109/CISS.2008.4558489},
Key = {fds287182}
}

@article{fds287181,
Author = {Daubechies, I and Teschke, G and Vese, L},
Title = {On some iterative concepts for image restoration},
Journal = {Advances in Imaging and Electron Physics},
Volume = {150},
Pages = {1-51},
Publisher = {Elsevier},
Year = {2008},
Month = {January},
ISSN = {1076-5670},
url = {http://dx.doi.org/10.1016/S1076-5670(07)00001-8},
Abstract = {Several iterative strategies for solving inverse problems in
the context of signal and image processing are discussed.
Problems for which it is reasonable to assume that the
solution has a sparse expansion with respect to a wavelet
basis or frame are focused. A variational formulation of the
problem is considered and an iteration scheme for which the
iterates approximate the solution is constructed. The
concrete problem of simultaneously denoising, decomposing,
and deblurring a given image, is discussed. The associated
variational formulation of the problem contains terms that
promote sparsity and smoothness. A natural extension to
vector-valued inverse problems is also considered. In the
linear case, and under fairly general assumptions on the
constraint, its is proved that weak convergence of the
iterative scheme always holds.},
Doi = {10.1016/S1076-5670(07)00001-8},
Key = {fds287181}
}

@article{fds287184,
Author = {Johnson, CR and Hendriks, E and Berezhnoy, IJ and Brevdo, E and Hughes,
SM and Daubechies, I and Li, J and Postma, E and Wang,
JZ},
Title = {Image processing for artist identification: Computerized
analysis of Vincent van Gogh's painting brushstrokes},
Journal = {Ieee Signal Processing Magazine},
Volume = {25},
Number = {4},
Pages = {37-48},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2008},
Month = {January},
ISSN = {1053-5888},
url = {http://dx.doi.org/10.1109/MSP.2008.923513},
Abstract = {A description on the approaches to brushwork analysis and
artist identification within the framework of data set is
given. Image processing is now a reality in painting
analysis as high resolution and richer data are also
available. A summary on the results that are obtained by
several groups are presented who uses wavelet decomposition
of the same data set. Better results can easily be achieved
with the use of wider range of signal analysis tools.
Furthermore, there is a growth within interested
researchers, targeted conference sessions, and specialist
workshops regarding painting analysis.},
Doi = {10.1109/MSP.2008.923513},
Key = {fds287184}
}

@article{fds287180,
Author = {Rudin, C and Schapire, RE and Daubechies, I},
Title = {Analysis of boosting algorithms using the smooth margin
function},
Journal = {The Annals of Statistics},
Volume = {35},
Number = {6},
Pages = {2723-2768},
Publisher = {Institute of Mathematical Statistics},
Year = {2007},
Month = {December},
ISSN = {0090-5364},
url = {http://dx.doi.org/10.1214/009053607000000785},
Abstract = {We introduce a useful tool for analyzing boosting algorithms
called the "smooth margin function," a differentiable
approximation of the usual margin for boosting algorithms.
We present two boosting algorithms based on this smooth
margin, "coordinate ascent boosting" and "approximate
coordinate ascent boosting," which are similar to Freund and
Schapire's AdaBoost algorithm and Breiman's arc-gv
algorithm. We give convergence rates to the maximum margin
solution for both of our algorithms and for arc-gv. We then
study AdaBoost's convergence properties using the smooth
margin function. We precisely bound the margin attained by
AdaBoost when the edges of the weak classifiers fall within
a specified range. This shows that a previous bound proved
by Ratsch and Warmuth is exactly tight. Furthermore, we use
the smooth margin to capture explicit properties of AdaBoost
in cases where cyclic behavior occurs. © Institute of
Mathematical Statistics, 2007.},
Doi = {10.1214/009053607000000785},
Key = {fds287180}
}

@article{fds287179,
Author = {Cvetkovic, Z and Daubechies, I and Logan, BF},
Title = {Single-bit oversampled A/D conversion with exponential
accuracy in the bit rate},
Journal = {Ieee Transactions on Information Theory},
Volume = {53},
Number = {11},
Pages = {3979-3989},
Year = {2007},
Month = {November},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2007.907508},
Abstract = {A scheme for simple oversampled analog-to-digital (A/D)
conversion using single-bit quantization is presented. The
scheme is based on recording positions of zero-crossings of
the input signal added to a deterministic dither function.
This information can be represented in a manner such that
the bit rate increases only logarithmically with the
oversampling factor r. The input band-limited signal can be
reconstructed from this information locally with O(1/r)
pointwise error, resulting in an exponentially decaying
distortion-rate characteristic. In the course of studying
the accuracy of the proposed A/D conversion scheme, some new
results are established about reconstruction of band-limited
signals from irregular samples using linear combination of
functions with fast decay. Schemes for local interpolation
of band-limited signals from quantized irregular samples are
Doi = {10.1109/TIT.2007.907508},
Key = {fds287179}
}

@article{fds287177,
Author = {Daubechies, I and Runborg, O and Zou, J},
Title = {A sparse spectral method for homogenization multiscale
problems},
Journal = {Multiscale Modeling & Simulation},
Volume = {6},
Number = {3},
Pages = {711-740},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2007},
Month = {August},
ISSN = {1540-3459},
url = {http://dx.doi.org/10.1137/060676258},
Abstract = {We develop a new sparse spectral method, in which the fast
Fourier transform (FFT) is replaced by RAℓSFA (randomized
algorithm of sparse Fourier analysis); this is a sublinear
randomized algorithm that takes time O(B log N) to recover a
B-term Fourier representation for a signal of length N,
where we assume B ≪ N. To illustrate its potential, we
consider the parabolic homogenization problem with a
characteristic fine scale size ε. For fixed tolerance the
sparse method has a computational cost of O( logε ) per
time step, whereas standard methods cost at least O(ε-1).
We present a theoretical analysis as well as numerical
results; they show the advantage of the new method in speed
over the traditional spectral methods when ε is very small.
We also show some ways to extend the methods to hyperbolic
and elliptic problems. © 2007 Society for Industrial and
Applied Mathematics.},
Doi = {10.1137/060676258},
Key = {fds287177}
}

@article{fds287178,
Author = {Loris, I and Nolet, G and Daubechies, I and Dahlen,
FA},
Title = {Tomographic inversion using ℓ1-norm
regularization of wavelet coefficients},
Journal = {Geophysical Journal International},
Volume = {170},
Number = {1},
Pages = {359-370},
Publisher = {Oxford University Press (OUP)},
Year = {2007},
Month = {July},
ISSN = {0956-540X},
url = {http://dx.doi.org/10.1111/j.1365-246X.2007.03409.x},
Abstract = {We propose the use of ℓ1 regularization in a wavelet basis
for the solution of linearized seismic tomography problems
Am = d, allowing for the possibility of sharp
discontinuities superimposed on a smoothly varying
background. An iterative method is used to find a sparse
solution m that contains no more fine-scale structure than
is necessary to fit the data d to within its assigned
RAS.},
Doi = {10.1111/j.1365-246X.2007.03409.x},
Key = {fds287178}
}

@article{fds287175,
Author = {Daubechies, I and Lazarsfeld, R and Morgan, J and Okounkov, A and Tao,
T},
Title = {Reply to Davey, Henriksen, Marković and Pratt
[4]},
Journal = {Notices of the American Mathematical Society},
Volume = {54},
Number = {6},
Pages = {694},
Year = {2007},
Month = {June},
ISSN = {0002-9920},
Key = {fds287175}
}

@article{fds335534,
Author = {Daubechies, I and Teschke, G and Vese, L},
Title = {Iteratively solving linear inverse problems under general
convex constraints},
Journal = {Inverse Problems and Imaging},
Volume = {1},
Number = {1},
Pages = {29-46},
Publisher = {American Institute of Mathematical Sciences
(AIMS)},
Year = {2007},
Month = {January},
url = {http://dx.doi.org/10.3934/ipi.2007.1.29},
Abstract = {© 2007 AIMSciences. We consider linear inverse problems
where the solution is assumed to fulfill some general
homogeneous convex constraint. We develop an algorithm that
amounts to a projected Landweber iteration and that provides
and iterative approach to the solution of this inverse
problem. For relatively moderate assumptions on the
constraint we can always prove weak convergence of the
iterative scheme. In certain cases, i.e. for special
families of convex constraints, weak convergence implies
norm convergence. The presented approach covers a wide range
of problems, e.g. Besov– or BV–restoration for which we
present also numerical experiments in the context of image
processing.},
Doi = {10.3934/ipi.2007.1.29},
Key = {fds335534}
}

@article{fds287171,
Author = {Hughes, SM and Daubechies, I},
Title = {Simpler alternatives to information theoretic similarity
metrics for multimodal image alignment},
Journal = {Proceedings International Conference on Image Processing,
Icip},
Pages = {365-368},
Publisher = {IEEE},
Year = {2006},
Month = {December},
ISSN = {1522-4880},
url = {http://dx.doi.org/10.1109/ICIP.2006.313169},
Abstract = {Mutual information (MI) based methods for image registration
enjoy great experimental success and are becoming widely
used. However, they impose a large computational burden that
limits their use; many applications would benefit from a
reduction of the computational load. Although the
theoretical justification for these methods draws upon the
stochastic concept of mutual information, in practice, such
methods actually seek the best alignment by maximizing a
number that is (deterministically) computed from the two
images. These methods thus optimize a fixed function, the
"similarity metric," over different candidate alignments of
the two images. Accordingly, we study the important features
of the computationally complex MI similarity metric with the
goal of distilling them into simpler surrogate functions
that are easier to compute. More precisely, we show that
maximizing the MI similarity metric is equivalent to
minimizing a certain distance metric between equivalence
classes of images, where images f and g are said to be
equivalent if there exists a bijection ø such that f (x) =
ø(g (x)) for all x. We then show how to design new
similarity metrics for image alignment with this property.
Although we preserve only this aspect of MI, our new metrics
show equal alignment accuracy and similar robustness to
noise, while significantly decreasing computation time. We
conclude that even the few properties of MI preserved by our
method suffice for accurate registration and may in fact be
responsible for MI's success. ©2006 IEEE.},
Doi = {10.1109/ICIP.2006.313169},
Key = {fds287171}
}

@article{fds287176,
Author = {Daubechies, I and Yilmaz, O},
Title = {Robust and practical analog-to-digital conversion with
exponential precision},
Journal = {Ieee Transactions on Information Theory},
Volume = {52},
Number = {8},
Pages = {3533-3545},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2006},
Month = {August},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2006.878220},
Abstract = {Beta-encoders with error correction were introduced by
Daubechies, DeVore, Güntürk and Vaishampayan as an
alternative to pulse-code modulation (PCM) for
analog-to-digital conversion. An N -bit beta-encoder
quantizes a real number by computing one of its N-bit
truncated β-expansions where β ∈ (1, 2) determines the
base of expansion. These encoders have (almost) optimal
rate-distortion properties like PCM; furthermore, they
exploit the redundancy of beta-expansions and thus they are
robust with respect to quantizer imperfections. However,
these encoders have the shortcoming that the decoder needs
to know the value of the base of expansion β, a gain factor
in the circuit used by the encoder, which is an impractical
constraint. We present a method to implement beta-encoders
so that they are also robust with respect to uncertainties
of the value of β. The method relies upon embedding the
value of β in the encoded bitstream.We show that this can
be done without a priori knowledge of β by the transmitting
party. Moreover the algorithm still works if the value of β
changes (slowly) during the implementation. © 2006
IEEE.},
Doi = {10.1109/TIT.2006.878220},
Key = {fds287176}
}

@article{fds287174,
Author = {Daubechies, I and DeVore, RA and Güntürk, CS and Vaishampayan,
VA},
Title = {A/D conversion with imperfect quantizers},
Journal = {Ieee Transactions on Information Theory},
Volume = {52},
Number = {3},
Pages = {874-885},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2006},
Month = {March},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2005.864430},
Abstract = {This paper analyzes mathematically the effect of quantizer
threshold imperfection commonly encountered in the circuit
implementation of analog-to-digltal (A/D) converters such as
pulse code modulation (PCM) and sigma-delta (∑Δ)
modulation. ∑Δ modulation, which is based on coarse
quantization of oversampled (redundant) samples of a signal,
enjoys a type of self-correction property for quantizer
threshold errors (bias) that is not shared by PCM. Although
"classical" ∑Δ modulation is inferior to PCM in the
rate-distortion sense, this robustness feature is believed
to be one of the reasons why ∑Δ modulation is preferred
over PCM in A/D converters with imperfect quantizers.
Motivated by these facts, other encoders are constructed in
this paper that use redundancy to obtain a similar
self-correction property, but that achieve higher order
accuracy relative to bit rate compared to classical ∑Δ.
More precisely, two different types of encoders are
introduced that exhibit exponential accuracy in the bit rate
(in contrast to the polynomial-type accuracy of classical
∑Δ) while possessing the self-correction property. ©
2006 IEEE.},
Doi = {10.1109/TIT.2005.864430},
Key = {fds287174}
}

@article{fds287173,
Author = {Zou, J and Gilbert, A and Strauss, M and Daubechies,
I},
Title = {Theoretical and experimental analysis of a randomized
algorithm for Sparse Fourier transform analysis},
Journal = {Journal of Computational Physics},
Volume = {211},
Number = {2},
Pages = {572-595},
Publisher = {Elsevier BV},
Year = {2006},
Month = {January},
url = {http://dx.doi.org/10.1016/j.jcp.2005.06.005},
Abstract = {We analyze a sublinear RAℓSFA (randomized algorithm for
Sparse Fourier analysis) that finds a near-optimal B-term
Sparse representation R for a given discrete signal S of
length N, in time and space poly (B, log(N)), following the
approach given in [A.C. Gilbert, S. Guha, P. Indyk, S.
Muthukrishnan, M. Strauss, Near-Optimal Sparse Fourier
Representations via Sampling, STOC, 2002]. Its time cost
poly (log(N)) should be compared with the superlinear Ω(N
log N) time requirement of the Fast Fourier Transform (FFT).
A straightforward implementation of the RAℓSFA, as
presented in the theoretical paper [A.C. Gilbert, S. Guha,
P. Indyk, S. Muthukrishnan, M. Strauss, Near-Optimal Sparse
Fourier Representations via Sampling, STOC, 2002], turns out
to be very slow in practice. Our main result is a greatly
improved and practical RAℓSFA. We introduce several new
ideas and techniques that speed up the algorithm. Both
rigorous and heuristic arguments for parameter choices are
presented. Our RAℓSFA constructs, with probability at
least 1 - δ, a near-optimal B-term representation R in time
poly(B) log(N) log(1/δ)/ε2 log(M) such that ∥S - R∥22
≤ (1 + ε) ∥S - Ropt∥22. Furthermore, this RAℓSFA
implementation already beats the FFTW for not unreasonably
large N. We extend the algorithm to higher dimensional cases
both theoretically and numerically. The crossover point lies
at N ≃ 70, 000 in one dimension, and at N ≃ 900 for data
on a N × N grid in two dimensions for small B signals where
there is noise. © 2005 Elsevier Inc. All rights
reserved.},
Doi = {10.1016/j.jcp.2005.06.005},
Key = {fds287173}
}

@article{fds287172,
Author = {Roussos, E and Roberts, S and Daubechies, I},
Title = {Variational Bayesian learning for wavelet independent
component analysis},
Journal = {Aip Conference Proceedings},
Volume = {803},
Pages = {274-281},
Publisher = {AIP},
Year = {2005},
Month = {November},
ISSN = {0094-243X},
url = {http://dx.doi.org/10.1063/1.2149805},
Abstract = {In an exploratory approach to data analysis, it is often
useful to consider the observations as generated from a set
of latent generators or "sources" via a generally unknown
mapping. For the noisy overcomplete case, where we have more
sources than observations, the problem becomes extremely
ill-posed. Solutions to such inverse problems can, in many
cases, be achieved by incorporating prior knowledge about
the problem, captured in the form of constraints. This
setting is a natural candidate for the application of the
Bayesian methodology, allowing us to incorporate "soft"
constraints in a natural manner. The work described in this
paper is mainly driven by problems in functional magnetic
resonance imaging of the brain, for the neuro-scientific
goal of extracting relevant "maps" from the data. This can
be stated as a 'blind' source separation problem. Recent
experiments in the field of neuroscience show that these
maps are sparse, in some appropriate sense. The separation
problem can be solved by independent component analysis
(ICA), viewed as a technique for seeking sparse components,
assuming appropriate distributions for the sources. We
derive a hybrid wavelet-ICA model, transforming the signals
into a domain where the modeling assumption of sparsity of
the coefficients with respect to a dictionary is natural. We
follow a graphical modeling formalism, viewing ICA as a
probabilistic generative model. We use hierarchical source
and mixing models and apply Bayesian inference to the
problem. This allows us to perform model selection in order
to infer the complexity of the representation, as well as
automatic denoising. Since exact inference and learning in
such a model is intractable, we follow a variational
Bayesian mean-field approach in the conjugate-exponential
family of distributions, for efficient unsupervised learning
in multi-dimensional settings. The performance of the
proposed algorithm is demonstrated on some representative
experiments. © 2005 American Institute of
Physics.},
Doi = {10.1063/1.2149805},
Key = {fds287172}
}

@article{fds287170,
Author = {Daubechies, I and Teschke, G},
Title = {Variational image restoration by means of wavelets:
Simultaneous decomposition, deblurring, and
denoising},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {19},
Number = {1},
Pages = {1-16},
Publisher = {Elsevier BV},
Year = {2005},
Month = {July},
url = {http://dx.doi.org/10.1016/j.acha.2004.12.004},
Abstract = {Inspired by papers of Vese-Osher [Modeling textures with
total variation minimization and oscillating patterns in
image processing, Technical Report 02-19, 2002] and
Osher-Solé-Vese [Image decomposition and restoration using
total variation minimization and the H-1 norm, Technical
Report 02-57, 2002] we present a wavelet-based treatment of
variational problems arising in the field of image
processing. In particular, we follow their approach and
discuss a special class of variational functionals that
induce a decomposition of images into oscillating and
cartoon components and possibly an appropriate 'noise'
component. In the setting of [Modeling textures with total
variation minimization and oscillating patterns in image
processing, Technical Report 02-19, 2002] and [Image
decomposition and restoration using total variation
minimization and the H-1 norm, Technical Report 02-57,
2002], the cartoon component of an image is modeled by a BV
function; the corresponding incorporation of BV penalty
terms in the variational functional leads to PDE schemes
that are numerically intensive. By replacing the BV penalty
term by a B11(L1) term (which amounts to a slightly stronger
constraint on the minimizer), and writing the problem in a
wavelet framework, we obtain elegant and numerically
efficient schemes with results very similar to those
obtained in [Modeling textures with total variation
minimization and oscillating patterns in image processing,
Technical Report 02-19, 2002] and [Image decomposition and
restoration using total variation minimization and the H-1
norm, Technical Report 02-57, 2002]. This approach allows
us, moreover, to incorporate general bounded linear blur
operators into the problem so that the minimization leads to
a simultaneous decomposition, deblurring and denoising. ©
Doi = {10.1016/j.acha.2004.12.004},
Key = {fds287170}
}

@article{fds287168,
Author = {Pierpaoli, E and Anthoine, S and Huffenberger, K and Daubechies,
I},
Title = {Reconstructing Sunyaev-Zel'dovich clusters in future cosmic
microwave background experiments},
Journal = {Monthly Notices of the Royal Astronomical
Society},
Volume = {359},
Number = {1},
Pages = {261-271},
Publisher = {Oxford University Press (OUP)},
Year = {2005},
Month = {May},
url = {http://dx.doi.org/10.1111/j.1365-2966.2005.08896.x},
Abstract = {We present a new method for component separation aimed at
extracting Sunyaev-Zel'dovich (SZ) galaxy clusters from
multifrequency maps of cosmic microwave background (CMB)
experiments. This method is designed to recover
non-Gaussian, spatially localized and sparse signals. We
first characterize the cluster non-Gaussianity by studying
it on simulated SZ maps. We then apply our estimator on
simulated observations of the Planck and Atacama Cosmology
Telescope (ACT) experiments. The method presented here
outperforms multifrequency Wiener filtering, both in the
reconstructed average intensity for given input and in the
associated error. In the absence of point source
contamination, this technique reconstructs the ACT (Planck)
bright (big) cluster central y parameter with an intensity
that is about 84 (43) per cent of the original input value.
The associated error in the reconstruction is about 12 and
27 per cent for the 50 (12) ACT (Planck) clusters
considered. For ACT, the error is dominated by beam
smearing. In the Planck case, the error in the
reconstruction is largely determined by the noise level: a
noise reduction by a factor of 7 would imply almost perfect
reconstruction and 10 per cent error for a large sample of
clusters. We conclude that the selection function of Planck
clusters will strongly depend on the noise properties in
different sky regions, as well as the specific cluster
extraction method assumed. © 2005 RAS.},
Doi = {10.1111/j.1365-2966.2005.08896.x},
Key = {fds287168}
}

@article{fds287102,
Author = {Daubechies, I and Lieb, EH},
Title = {One-electron relativistic molecules with coulomb
interaction},
Pages = {471-484},
Publisher = {Springer Verlag},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.1007/3-540-27056-6_33},
Abstract = {As an approximation to a relativistic one-electron molecule,
we study the operator H=(-Δ+m2)1/2-e2 Z j|x-Rj|-1 with Zj0,
e -2=137.04. H is bounded below if and only if e2 Z j>2/π,
all j. Assuming this condition, the system is unstable when
e2ΣZj>2/π in the sense that E 0=inf spec (H) → - ∞ as
the Rj → 0, all j. We prove that the nuclear Coulomb
repulsion more than restores stability; namely E0+0.069e2
ZiZj|R i-Rj|-10. We also show that E0 is an increasing
function of the internuclear distances |Ri-R j|. © 2005
Springer-Verlag Berlin Heidelberg New York.},
Doi = {10.1007/3-540-27056-6_33},
Key = {fds287102}
}

@article{fds287107,
Author = {Daubechies, I and Drakakis, K and Khovanova, T},
Title = {A detailed study of the attachment strategies of new
autonomous systems in the as connectivity
graph},
Journal = {Internet Mathematics},
Volume = {2},
Number = {2},
Pages = {185-246},
Publisher = {Internet Mathematics},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.1080/15427951.2005.10129103},
Abstract = {© A K Peters, Ltd. The connectivity of the autonomous
systems (ASs) in the Internet can be modeled as a
time-evolving random graph, whose nodes represent ASs and
whose edges represent direct connections between them. Even
though this graph has some random aspects, its properties
show it to be fundamentally different from “traditional”
random graphs. In the first part of this paper, we use real
BGP data to study some properties of the AS connectivity
graph and its evolution in time. In the second part, we
build a simple model that is inspired by observations made
in the first part, and we discuss simulations of this
model.},
Doi = {10.1080/15427951.2005.10129103},
Key = {fds287107}
}

@article{fds287166,
Author = {Rudin, C and Schapire, RE and Daubechies, I},
Title = {Boosting based on a smooth margin},
Journal = {Lecture Notes in Computer Science (Including Subseries
Lecture Notes in Artificial Intelligence and Lecture Notes
in Bioinformatics)},
Volume = {3120},
Pages = {502-517},
Publisher = {Springer Berlin Heidelberg},
Year = {2004},
Month = {December},
ISSN = {0302-9743},
url = {http://dx.doi.org/10.1007/978-3-540-27819-1_35},
Abstract = {We study two boosting algorithms, Coordinate Ascent Boosting
and Approximate Coordinate Ascent Boosting, which are
explicitly designed to produce maximum margins. To derive
these algorithms, we introduce a smooth approximation of the
margin that one can maximize in order to produce a maximum
margin classifier. Our first algorithm is simply coordinate
ascent on this function, involving a line search at each
step. We then make a simple approximation of this line
search to reveal our second algorithm. These algorithms are
proven to asymptotically achieve maximum margins, and we
provide two convergence rate calculations. The second
calculation yields a faster rate of convergence than the
first, although the first gives a more explicit (still fast)
rate. These algorithms are very similar to AdaBoost in that
they are based on coordinate ascent, easy to implement, and
empirically tend to converge faster than other boosting
algorithms. Finally, we attempt to understand AdaBoost in
terms of our smooth margin, focusing on cases where AdaBoost
exhibits cyclic behavior.},
Doi = {10.1007/978-3-540-27819-1_35},
Key = {fds287166}
}

@article{fds287109,
Author = {Rudin, C and Daubechies, I and Schapire, RE},
Title = {The dynamics of AdaBoost: Cyclic behavior and convergence of
margins},
Journal = {Journal of Machine Learning Research},
Volume = {5},
Pages = {1557-1595},
Year = {2004},
Month = {December},
Abstract = {© 2004 Cynthia Rudin, Ingrid Daubechies and Robert E.
Schapire. In order to study the convergence properties of
iterated map and study the evolution of its weight vectors.
This dynamical systems approach allows us to understand
AdaBoost's convergence properties completely in certain
cases; for these cases we find stable cycles, allowing us to
explicitly solve for AdaBoost's output. Using this unusual
technique, we are able to show that AdaBoost does not always
converge to a maximum margin combined classifier, answering
an open question. In addition, we show that "nonoptimal"
AdaBoost (where the weak learning algorithm does not
necessarily choose the best weak classifier at each
iteration) may fail to converge to a maximum margin
classifier, even if "optimal" AdaBoost produces a maximum
margin. Also, we show that if AdaBoost cycles, it cycles
among "support vectors", i.e., examples that achieve the
same smallest margin.},
Key = {fds287109}
}

@article{fds287169,
Author = {Daubechies, I and Defrise, M and De Mol and C},
Title = {An iterative thresholding algorithm for linear inverse
problems with a sparsity constraint},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {57},
Number = {11},
Pages = {1413-1457},
Publisher = {WILEY},
Year = {2004},
Month = {November},
url = {http://dx.doi.org/10.1002/cpa.20042},
Abstract = {We consider linear inverse problems where the solution is
assumed to have a sparse expansion on an arbitrary
preassigned orthonormal basis. We prove that replacing the
usual quadratic regularizing penalties by weighted of ℓP -
penalties on the coefficients of such expansions, with 1 ≤
p ≤ 2, still regularizes the problem. Use of such ℓP-
penalized problems with p < 2 is often advocated when one
expects the underlying ideal noiseless solution to have a
sparse expansion with respect to the basis under
consideration. To compute the corresponding regularized
solutions, we analyze an iterative algorithm that amounts to
a Landweber iteration with thresholding (or nonlinear
shrinkage) applied at each iteration step. We prove that
this algorithm converges in norm. © 2004 Wiley Periodicals,
Inc.},
Doi = {10.1002/cpa.20042},
Key = {fds287169}
}

@article{fds287163,
Author = {Daubechies, I and Teschke, G},
Title = {Wavelet based image decomposition by variational
functionals},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {5266},
Pages = {94-105},
Publisher = {SPIE},
Year = {2004},
Month = {May},
url = {http://dx.doi.org/10.1117/12.516051},
Abstract = {We discuss a wavelet based treatment of variational problems
arising in the context of image processing, inspired by
papers of Vese-Osher and Osher-Solé-Vese, in particular, we
introduce a special class of variational functionals, that
induce a decomposition of images in oscillating and cartoon
components. Cartoons are often modeled by BV functions. In
the setting of Vese et.el. and Osher et.al. the
incorporation of BV penalty terms leads to PDE schemes that
are numerically intensive. We propose to embed the problem
in a wavelet framework. This provides us with elegant and
numerically efficient schemes even though a basic
requirement, the involvement of the space BV, has to be
softened slightly. We show results on test images of our
wavelet algorithm with a B11(L1) penalty term, and we
compare them with the BV restorations of
Osher-Solé-Vese.},
Doi = {10.1117/12.516051},
Key = {fds287163}
}

@article{fds287108,
Author = {Rudin, C and Daubechies, I and Schapire, RE},
Title = {On the dynamics of boosting},
Journal = {Advances in Neural Information Processing
Systems},
Pages = {1101-1108},
Publisher = {M I T PRESS},
Editor = {Thrun, S and Saul, LK and Schölkopf, B},
Year = {2004},
Month = {January},
ISBN = {0262201526},
Abstract = {In order to understand AdaBoost's dynamics, especially its
ability to maximize margins, we derive an associated
simplified nonlinear iterated map and analyze its behavior
in low-dimensional cases. We find stable cycles for these
cases, which can explicitly be used to solve for Ada-
Boost's output. By considering AdaBoost as a dynamical
system, we are able to prove R̈atsch and Warmuth's
conjecture that AdaBoost may fail to converge to a
maximal-margin combined classifier when given a 'nonoptimal'
weak learning algorithm. AdaBoost is known to be a
coordinate descent method, but other known algorithms that
explicitly aim to maximize the margin (such as AdaBoost and
arc-gv) are not. We consider a differentiable function for
which coordinate ascent will yield a maximum margin
solution. We then make a simple approximation to derive a
new boosting algorithm whose updates are slightly more
aggressive than those of arcgv.},
Key = {fds287108}
}

@article{fds287165,
Author = {Daubechies, I and Han, B},
Title = {Pairs of dual wavelet frames from any two refinable
functions},
Journal = {Constructive Approximation},
Volume = {20},
Number = {3},
Pages = {325-352},
Publisher = {Springer Nature},
Year = {2004},
Month = {January},
url = {http://dx.doi.org/10.1007/s00365-004-0567-4},
Abstract = {Starting from any two compactly supported refutable
functions in L 2 (R) with dilation factor d, we show that it
is always possible to construct 2d wavelet functions with
compact support such that they generate a pair of dual
d-wavelet frames in L2 (R). Moreover, the number of
vanishing moments of each of these wavelet frames is equal
to the approximation order of the dual MRA; this is the
highest possible. In particular, when we consider symmetric
refinable functions, the constructed dual wavelets are also
symmetric or antisymmetric. As a consequence, for any
compactly supported refinable function φ in L2 (R), it is
possible to construct, explicitly and easily, wavelets that
are finite linear combinations of translates φ(d -k), and
that generate a wavelet frame with an arbitrarily
preassigned number of vanishing moments. We illustrate the
general theory by examples of such pairs of dual wavelet
frames derived from B-spline functions.},
Doi = {10.1007/s00365-004-0567-4},
Key = {fds287165}
}

@article{fds287167,
Author = {Daubechies, I and Runborg, O and Sweldens, W},
Title = {Normal multiresolution approximation of curves},
Journal = {Constructive Approximation},
Volume = {20},
Number = {3},
Pages = {399-463},
Publisher = {Springer Nature},
Year = {2004},
Month = {January},
url = {http://dx.doi.org/10.1007/s00365-003-0543-4},
Abstract = {A multiresolution analysis of a curve is normal if each
wavelet detail vector with respect to a certain subdivision
scheme lies in the local normal direction. In this paper we
study properties such as regularity, convergence, and
stability of a normal multiresolution analysis. In
particular, we show that these properties critically depend
on the underlying subdivision scheme and that, in general,
the convergence of normal multiresolution approximations
equals the convergence of the underlying subdivision
scheme.},
Doi = {10.1007/s00365-003-0543-4},
Key = {fds287167}
}

@article{fds287161,
Author = {Daubechies, I and Han, B and Ron, A and Shen, Z},
Title = {Framelets: MRA-based constructions of wavelet
frames},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {14},
Number = {1},
Pages = {1-46},
Publisher = {Elsevier BV},
Year = {2003},
Month = {January},
url = {http://dx.doi.org/10.1016/S1063-5203(02)00511-0},
Abstract = {We discuss wavelet frames constructed via multiresolution
analysis (MRA), with emphasis on tight wavelet frames. In
particular, we establish general principles and specific
algorithms for constructing framelets and tight framelets,
and we show how they can be used for systematic
constructions of spline, pseudo-spline tight frames, and
symmetric bi-frames with short supports and high
approximation orders. Several explicit examples are
discussed. The connection of these frames with
multiresolution analysis guarantees the existence of fast
implementation algorithms, which we discuss briefly as well.
© 2002 Elsevier Science (USA). All rights
reserved.},
Doi = {10.1016/S1063-5203(02)00511-0},
Key = {fds287161}
}

@article{fds287162,
Author = {Cohen, A and Dahmen, W and Daubechies, I and DeVore,
R},
Title = {Harmonic analysis of the space BV},
Journal = {Revista Matemática Iberoamericana},
Volume = {19},
Number = {1},
Pages = {235-263},
Publisher = {European Mathematical Publishing House},
Year = {2003},
Month = {January},
url = {http://dx.doi.org/10.4171/RMI/345},
Abstract = {We establish new results on the space BV of functions with
bounded variation. While it is well known that this space
admits no unconditional basis, we show that it is "almost"
characterized by wavelet expansions in the following sense:
if a function f is in BV, its coefficient sequence in a BV
normalized wavelet basis satisfies a class of weak-l1 type
estimates. These weak estimates can be employed to prove
many interesting results. We use them to identify the
interpolation spaces between BV and Sobolev or Besov spaces,
and to derive new Gagliardc-Nirenberg-type
inequalities.},
Doi = {10.4171/RMI/345},
Key = {fds287162}
}

@article{fds287164,
Author = {Daubechies, I and Devore, R},
Title = {Approximating a bandlimited function using very coarsely
quantized data: A family of stable sigma-delta modulators of
arbitrary order},
Journal = {Annals of Mathematics},
Volume = {158},
Number = {2},
Pages = {679-710},
Publisher = {Annals of Mathematics, Princeton U},
Year = {2003},
Month = {January},
ISSN = {0003-486X},
url = {http://dx.doi.org/10.4007/annals.2003.158.679},
Doi = {10.4007/annals.2003.158.679},
Key = {fds287164}
}

@article{fds287159,
Author = {Daubechies, I and Planchon, F},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {13},
Number = {1},
Pages = {1-21},
Publisher = {Elsevier BV},
Year = {2002},
Month = {July},
url = {http://dx.doi.org/10.1016/S1063-5203(02)00003-9},
Abstract = {We aim to provide time-frequency representations of a
one-dimensional signal where the window is locally adapted
to the signal, thus providing a better readability of the
representation. © 2002 Elsevier Science (USA). All rights
reserved.},
Doi = {10.1016/S1063-5203(02)00003-9},
Key = {fds287159}
}

@article{fds287160,
Author = {Cohen, A and Daubechies, I and Guleryuz, OG and Orchard,
MT},
Title = {On the importance of combining wavelet-based nonlinear
approximation with coding strategies},
Journal = {Ieee Transactions on Information Theory},
Volume = {48},
Number = {7},
Pages = {1895-1921},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2002},
Month = {July},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2002.1013132},
Abstract = {This paper provides a mathematical analysis of transform
compression in its relationship to linear and nonlinear
approximation theory. Contrasting linear and nonlinear
approximation spaces, we show that there are interesting
classes of functions/random processes which are much more
compactly represented by wavelet-based nonlinear
approximation. These classes include locally smooth signals
that have singularities, and provide a model for many
signals encountered in practice, in particular for images.
However, we also show that nonlinear approximation results
do not always translate to efficient compression strategies
in a rate-distortion sense. Based on this observation, we
construct compression techniques and formulate the family of
functions/stochastic processes for which they provide
efficient descriptions in a rate-distortion sense. We show
that this family invariably leads to Besov spaces, yielding
a natural relationship among Besov smoothness,
linear/nonlinear approximation order, and compression
performance in a rate-distortion sense. The designed
compression techniques show similarities to modern
high-performance transform codecs, allowing us to establish
relevant rate-distortion estimates and identify performance
limits.},
Doi = {10.1109/TIT.2002.1013132},
Key = {fds287160}
}

@article{fds287206,
Author = {Calderbank, AR and Daubechies, I},
Title = {The pros and cons of democracy},
Journal = {Ieee Transactions on Information Theory},
Volume = {48},
Number = {6},
Pages = {1721-1725},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2002},
Month = {June},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/TIT.2002.1003852},
Abstract = {The concept of democracy was introduced in which the
individual bits in a coarsely quantized representation of a
signal were given equal weight in the approximation to the
original signal. It was proved that such democratic
representations could not achieve the same accuracy as
optimal nondemocratic schemes. Convolutional decoding was
found to be convenient in digital to analog
conversion.},
Doi = {10.1109/TIT.2002.1003852},
Key = {fds287206}
}

@article{fds287158,
Author = {Daubechies, I and Han, B},
Title = {The canonical dual frame of a wavelet frame},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {12},
Number = {3},
Pages = {269-285},
Year = {2002},
Month = {May},
ISSN = {1063-5203},
url = {http://dx.doi.org/10.1006/acha.2002.0381},
Abstract = {In this paper we show that there exist wavelet frames that
have nice dual wavelet frames, but for which the canonical
dual frame does not consist of wavelets, i.e., cannot be
generated by the translates and dilates of a single
function. © 2002 Elsevier Science (USA).},
Doi = {10.1006/acha.2002.0381},
Key = {fds287158}
}

@article{fds287156,
Author = {Daubechies, I and DeVore, R and Güntürk, CS and Vaishampayan,
VA},
Title = {Beta expansions: A new approach to digitally corrected A/D
conversion},
Journal = {Proceedings Ieee International Symposium on Circuits and
Systems},
Volume = {2},
Pages = {784-787},
Publisher = {IEEE},
Year = {2002},
Month = {January},
url = {http://dx.doi.org/10.1109/ISCAS.2002.1011470},
Abstract = {We introduce a new architecture for pipelined (and also
algorithmic) A/D converters that give exponentially accurate
conversion using inaccurate comparators. An error analysis
of a sigma-delta converter with an imperfect comparator and
a constant input reveals a self-correction property that is
not inherited by the successive refinement quantization
algorithm that underlies both pipelined multistage A/D
converters as well as algorithmic A/D converters. Motivated
by this example, we introduce a new A/D converter- the Beta
Converter-which has the same self-correction property as a
sigma-delta converter but which exhibits higher order
(exponential) accuracy with respect to the bit rate as
compared to a sigma-delta converter, which exhibits only
polynomial accuracy.},
Doi = {10.1109/ISCAS.2002.1011470},
Key = {fds287156}
}

@article{fds330516,
Author = {Cvetković, Z and Daubechies, I and Logan, BF},
Title = {Interpolation of bandlimited functions from quantized
irregular samples},
Journal = {Data Compression Conference Proceedings},
Volume = {2002-January},
Pages = {412-421},
Publisher = {IEEE Comput. Soc},
Year = {2002},
Month = {January},
ISBN = {0769514774},
url = {http://dx.doi.org/10.1109/DCC.2002.999981},
Abstract = {© 2002 IEEE. The problem of reconstructing a π-bandlimited
signal f from its quantized samples taken at an irregular
sequence of points (tk)k∈ZZ arises in oversampled
analog-to-digital conversion. The input signal can be
reconstructed from the quantized samples (f(tk))k∈ZZ by
estimating samples (f(n/λ))n∈ZZ, where λ is the average
uniform density of the sequence (tk)k∈ZZ, assumed here to
be greater than one, followed by linear low-pass filtering.
We study three techniques for estimating samples
(f(n/λ))n∈ZZ from quantized irregular samples
(f(tk))k∈ZZ, including Lagrangian interpolation, and two
other techniques which result in a better overall accuracy
of oversampled A/D conversion.},
Doi = {10.1109/DCC.2002.999981},
Key = {fds330516}
}

@article{fds287155,
Author = {Daubechies, I and Guskov, I and Sweldens, W},
Title = {Commutation for irregular subdivision},
Journal = {Constructive Approximation},
Volume = {17},
Number = {4},
Pages = {479-513},
Publisher = {Springer Nature},
Year = {2001},
Month = {December},
url = {http://dx.doi.org/10.1007/s00365-001-0001-0},
Abstract = {We present a generalization of the commutation formula to
irregular subdivision schemes and wavelets. We show how, in
the noninterpolating case, the divided differences need to
be adapted to the subdivision scheme. As an example we
include the construction of an entire family of biorthogonal
compactly supported irregular knot B-spline wavelets
starting from Lagrangian interpolation.},
Doi = {10.1007/s00365-001-0001-0},
Key = {fds287155}
}

@article{fds287157,
Author = {Cohen, A and Dahmen, W and Daubechies, I and Devore,
R},
Title = {Tree Approximation and Optimal Encoding},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {11},
Number = {2},
Pages = {192-226},
Publisher = {Elsevier BV},
Year = {2001},
Month = {September},
url = {http://dx.doi.org/10.1006/acha.2001.0336},
Abstract = {Tree approximation is a new form of nonlinear approximation
which appears naturally in some applications such as image
processing and adaptive numerical methods. It is somewhat
more restrictive than the usual n-term approximation. We
show that the restrictions of tree approximation cost little
in terms of rates of approximation. We then use that result
to design encoders for compression. These encoders are
universal (they apply to general functions) and progressive
(increasing accuracy is obtained by sending bit stream
increments). We show optimality of the encoders in the sense
that they provide upper estimates for the Kolmogorov entropy
Doi = {10.1006/acha.2001.0336},
Key = {fds287157}
}

@article{fds287153,
Author = {Balan, R and Daubechies, I and Vaishampayan, V},
Title = {The analysis and design of windowed fourier frame based
multiple description source coding schemes},
Journal = {Ieee Transactions on Information Theory},
Volume = {46},
Number = {7},
Pages = {2491-2536},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2000},
Month = {December},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/18.887860},
Abstract = {In this paper the windowed Fourier encoding-decoding scheme
applied to the multiple description compression problem is
analyzed. In the general case, four window functions are
needed to define the encoder and decoder, although this
number can be reduced to three or two by using time-shift or
frequency-shift division schemes. The encoding coefficients
are next divided into two groups according to the eveness of
either modulation or translation index. The distortion on
each channel is analyzed using the Zak transform. For the
optimal windows, explicit representation formulas are
obtained and nonlocalization results are proved. Asymptotic
formulas of the total distortion and transmission rate are
established and the redundancy is shown to trade off between
Doi = {10.1109/18.887860},
Key = {fds287153}
}

@article{fds287154,
Author = {Cvetkovic, Z and Daubechies, I},
Title = {Single-bit oversampled A/D conversion with exponential
accuracy in the bit-rate},
Journal = {Data Compression Conference Proceedings},
Pages = {343-352},
Publisher = {IEEE Comput. Soc},
Year = {2000},
Month = {January},
ISSN = {1068-0314},
url = {http://dx.doi.org/10.1109/dcc.2000.838174},
Abstract = {We present a scheme for simple oversampled analog-to-digital
conversion, with single bit quantization and exponential
error decay in the bit-rate. The scheme is based on
recording positions of zero-crossings of the input signal
added to a deterministic dither function. This information
can be represented in a manner which requires only
logarithmic increase of the bit rate with the oversampling
factor, r. The input band-limited signal can be
reconstructed from this information locally, and with a mean
squared error which is inversely proportional to the square
of the oversampling factor. MSE = O (l/r 2). Consequently,
the mean squared error of this scheme exhibits exponential
decay in the bit-rate.},
Doi = {10.1109/dcc.2000.838174},
Key = {fds287154}
}

@article{fds287151,
Author = {Daubechies, I and Guskov, I and Schröder, P and Sweldens,
W},
Title = {Wavelets on irregular point sets},
Journal = {Philosophical Transactions. Series A, Mathematical,
Physical, and Engineering Sciences},
Volume = {357},
Number = {1760},
Pages = {2397-2413},
Publisher = {The Royal Society},
Year = {1999},
Month = {January},
ISSN = {1364-503X},
url = {http://dx.doi.org/10.1098/rsta.1999.0439},
analysing wavelets on irregular point sets in one and two
dimensions. We discuss current results on both the practical
and theoretical sides. In particular, we focus on
subdivision schemes and commutation rules. Several examples
are included.},
Doi = {10.1098/rsta.1999.0439},
Key = {fds287151}
}

@article{fds287152,
Author = {Daubechies, I and Guskov, I and Sweldens, W},
Title = {Regularity of irregular subdivision},
Journal = {Constructive Approximation},
Volume = {15},
Number = {3},
Pages = {381-426},
Year = {1999},
Month = {January},
url = {http://dx.doi.org/10.1007/s003659900114},
Abstract = {We study the smoothness of the limit function for
one-dimensional unequally spaced interpolating subdivision
schemes. The new grid points introduced at every level can
lie in irregularly spaced locations between old, adjacent
grid points and not only midway as is usually the case. For
the natural generalization of the four-point scheme
introduced by Dubuc and Dyn, Levin, and Gregory, we show
that, under some geometric restrictions, the limit function
is always C1; under slightly stronger restrictions we show
that the limit function is almost C2, the same regularity as
in the regularly spaced case.},
Doi = {10.1007/s003659900114},
Key = {fds287152}
}

@article{fds287145,
Author = {Donoho, DL and Vetterli, M and Devore, RA and Daubechies,
I},
Title = {Data compression and harmonic analysis},
Journal = {Ieee Transactions on Information Theory},
Volume = {44},
Number = {6},
Pages = {2435-2476},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1998},
Month = {December},
ISSN = {0018-9448},
url = {http://dx.doi.org/10.1109/18.720544},
Abstract = {In this paper we review some recent interactions between
harmonic analysis and data compression. The story goes back
of course to Shannon's R(D) theory in the case of Gaussian
stationary processes, which says that transforming into a
Fourier basis followed by block coding gives an optimal
lossy compression technique; practical developments like
transformbased image compression have been inspired by this
result. In this paper we also discuss connections perhaps
less familiar to the Information Theory community, growing
out of the field of harmonic analysis. Recent harmonic
analysis constructions, such as wavelet transforms and Gabor
transforms, are essentially optimal transforms for transform
coding in certain settings. Some of these transforms are
under consideration for future compression standards. We
discuss some of the lessons of harmonic analysis in this
century. Typically, the problems and achievements of this
field have involved goals that were not obviously related to
practical data compression, and have used a language not
immediately accessible to outsiders. Nevertheless, through
an extensive generalization of what Shannon called the
"sampling theorem," harmonic analysis has succeeded in
developing new forms of functional representation which turn
out to have significant data compression interpretations. We
explain why harmonic analysis has interacted with data
compression, and we describe some interesting recent ideas
in the field that may affect data compression in the future.
Doi = {10.1109/18.720544},
Key = {fds287145}
}

@article{fds287148,
Author = {Daubechies, I and Sweldens, W},
Title = {Factoring Wavelet Transforms into Lifting
Steps},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {4},
Number = {3},
Pages = {x1-268},
Year = {1998},
Month = {December},
any discrete wavelet transform or two band subband filtering
with finite filters can be decomposed into a finite sequence
of simple filtering steps, which we call lifting steps but
that are also known as ladder structures. This decomposition
corresponds to a factorization of the polyphase matrix of
the wavelet or subband filters into elementary matrices.
That such a factorization is possible is well-known to
algebraists (and expressed by the formula SL(n; R[z, z-1]) =
E(z; z-1])); it is also used in linear systems theory in the
electrical engineering community. We present here a
self-contained derivation, building the decomposition from
basic principles such as the Euclidean algorithm, with a
focus on applying it to wavelet filtering. This
factorization provides an alternative for the lattice
factorization, with the advantage that it can also be used
in the biorthogonal, i.e., non-unitary case. Like the
lattice factorization, the decomposition presented here
asymptotically reduces the computational complexity of the
transform by a factor two. It has other applications, such
as the possibility of defining a wavelet-like transform that
maps integers to integers.},
Key = {fds287148}
}

@article{fds287149,
Author = {Daubechies, I},
Title = {Preface},
Journal = {Wavelet Analysis and Its Applications},
Volume = {9},
Number = {C},
Pages = {5},
Year = {1998},
Month = {December},
ISSN = {1874-608X},
url = {http://dx.doi.org/10.1016/S1874-608X(98)80024-1},
Doi = {10.1016/S1874-608X(98)80024-1},
Key = {fds287149}
}

@article{fds287150,
Author = {Daubechies, I},
Title = {Recent results in wavelet applications},
Journal = {Journal of Electronic Imaging},
Volume = {7},
Number = {4},
Pages = {719-724},
Publisher = {SPIE-Intl Soc Optical Eng},
Year = {1998},
Month = {January},
ISSN = {1017-9909},
url = {http://dx.doi.org/10.1117/1.482659},
Abstract = {We present three recent developments in wavelets and
subdivision: wavelet-type transforms that map integers to
integers, with an application to lossless coding for images;
rate-distortion bounds that realize the compression given by
nonlinear approximation theorems for a model where wavelet
compression outperforms the Karhunen-Loève approach; and
smoothness results for irregularly spaced subdivision
schemes, related to wavelet compression for irregularly
spaced data. © 1998 SPIE and IS&T.},
Doi = {10.1117/1.482659},
Key = {fds287150}
}

@article{fds287205,
Author = {Calderbank, AR and Daubechies, I and Sweldens, W and Yeo,
BL},
Title = {Wavelet Transforms That Map Integers to Integers},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {5},
Number = {3},
Pages = {332-369},
Publisher = {Elsevier BV},
Year = {1998},
Month = {January},
url = {http://dx.doi.org/10.1006/acha.1997.0238},
Abstract = {Invertible wavelet transforms that map integers to integers
have important applications in lossless coding. In this
paper we present two approaches to build integer to integer
wavelet transforms. The first approach is to adapt the
precoder of Laroia et al., which is used in information
transmission; we combine it with expansion factors for the
high and low pass band in subband filtering. The second
approach builds upon the idea of factoring wavelet
transforms into socalled lifting steps. This allows the
construction of an integer version of every wavelet
transform. Finally, we use these approaches in a lossless
image coder and compare the results to those given in the
Doi = {10.1006/acha.1997.0238},
Key = {fds287205}
}

@article{fds287143,
Author = {Unser, M and Daubechies, I},
Title = {On the approximation power of convolution-based least
squares versus interpolation},
Journal = {Ieee Transactions on Signal Processing},
Volume = {45},
Number = {7},
Pages = {1697-1711},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1997},
Month = {December},
ISSN = {1053-587X},
url = {http://dx.doi.org/10.1109/78.599940},
Abstract = {There are many signal processing tasks for which
convolution-based continuous signal representations such as
splines and wavelets provide an interesting and practical
alternative to the more traditional sine-based methods. The
coefficients of the corresponding signal approximations are
typically obtained by direct sampling (interpolation or
quasiinterpolation) or by using least squares techniques
that apply a prefilter prior to sampling. Here, we compare
the performance of these approaches and provide quantitative
error estimates that can be used for the appropriate
selection of the sampling step h. Specifically, we review
several results in approximation theory with a special
emphasis on the Strang-Fix conditions, which relate the
general O(hL) behavior of the error to the ability of the
representation to reproduce polynomials of degree n -L -1.
We use this theory to derive pointwise error estimates for
the various algorithms and to obtain the asymptotic limit of
the LI -error as h tends to zero. We also propose a new
improved LI -error bound for the least squares case. In the
process, we provide all the relevant bound constants for
polynomial splines. Some of our results suggest the
existence of an intermediate range of sampling steps where
the least squares method is roughly equivalent to an
interpolator with twice the order. We present experimental
examples that illustrate the theory and confirm the adequacy
of our various bound and limit determinations. © 1997
IEEE.},
Doi = {10.1109/78.599940},
Key = {fds287143}
}

@article{fds287144,
Author = {Chassande-Mottin, E and Daubechies, I and Auger, F and Flandrin,
P},
Title = {Differential reassignment},
Journal = {Ieee Signal Processing Letters},
Volume = {4},
Number = {10},
Pages = {293-294},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1997},
Month = {December},
ISSN = {1070-9908},
url = {http://dx.doi.org/10.1109/97.633772},
Abstract = {A geometrical description is given for reassignment vector
fields of spectrograms. These vector fields are shown to be
connected with both an intrinsic phase characterization and
a scalar potential. This allows for the generalization of
the original reassignment process to a differential version
based on a dynamical evolution of time-frequency
particles.},
Doi = {10.1109/97.633772},
Key = {fds287144}
}

@article{fds287146,
Author = {Cohen, A and Daubechies, I and Plonka, G},
Title = {Regularity of Refinable Function Vectors},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {3},
Number = {3},
Pages = {x4-323},
Year = {1997},
Month = {December},
Abstract = {We study the existence and regularity of compactly supported
solutions φ = (φ ν ) ν=0r- 1 of vector refinement
equations. The space spanned by the translates of φ ν can
only provide approximation order if the refinement mask P
has certain particular factorization properties. We show,
how the factorization of P can lead to decay of |φ̂ ν
(u)| as |u| →∞. The results on decay are used to prove
uniqueness of solutions and convergence of the cascade
algorithm.},
Key = {fds287146}
}

@article{fds287147,
Author = {Daubechies, I},
Title = {From the Original Framer to Present-Day Time-Freuency and
Time-Scale Frames},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {3},
Number = {5},
Pages = {x1-486},
Year = {1997},
Month = {December},
Key = {fds287147}
}

@article{fds287204,
Author = {Calderbank, AR and Daubechies, I and Sweldens, W and Yeo,
BL},
Title = {Lossless image compression using integer to integer wavelet
transforms},
Journal = {Ieee International Conference on Image Processing},
Volume = {1},
Pages = {596-599},
Publisher = {IEEE Comput. Soc},
Year = {1997},
Month = {December},
url = {http://dx.doi.org/10.1109/icip.1997.647983},
Abstract = {Invertible wavelet transforms that map integers to integers
are important for lossless representations. In this paper,
we present an approach to build integer to integer wavelet
transforms based upon the idea of factoring wavelet
transforms into lifting steps. This allows the construction
of an integer version of every wavelet transform. We
demonstrate the use of these transforms in lossless image
compression.},
Doi = {10.1109/icip.1997.647983},
Key = {fds287204}
}

@article{fds287142,
Author = {Daubechies, I},
Title = {Where do wavelets come from? - a personal point of
view},
Journal = {Proceedings of the Ieee},
Volume = {84},
Number = {4},
Pages = {510-513},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1996},
Month = {April},
url = {http://dx.doi.org/10.1109/5.488696},
Abstract = {The subject area of wavelets is connected to older ideas in
many other fields, including pure and applied mathematics,
physics, computer science and engineering. The rapid
development of wavelet tools led to the application of
wavelets as a standard part of mathematical tool kits.
Developed wavelet tools also complemented more established
mathematical techniques. A wavelet transform was developed
from spline functions of harmonic analysis used in the
quantum field theory, wavelet decomposition for
multiresolution using recursive filtering algorithms and
Fourier transform with transform functions generated from a
Doi = {10.1109/5.488696},
Key = {fds287142}
}

@article{fds287140,
Author = {Cohen, A and Daubechies, I and Ron, A},
Title = {How smooth is the smoothest function in a given refinable
space?},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {3},
Number = {1},
Pages = {87-89},
Publisher = {Elsevier BV},
Year = {1996},
Month = {January},
url = {http://dx.doi.org/10.1006/acha.1996.0008},
Doi = {10.1006/acha.1996.0008},
Key = {fds287140}
}

@article{fds287141,
Author = {Cohen, A and Daubechies, I},
Title = {A new technique to estimate the regularity of refinable
functions},
Journal = {Revista Matemática Iberoamericana},
Volume = {12},
Number = {2},
Pages = {527-591},
Publisher = {European Mathematical Publishing House},
Year = {1996},
Month = {January},
url = {http://dx.doi.org/10.4171/RMI/207},
Abstract = {We study the regularity of refinable functions by analyzing
the spectral properties of special operators associated to
the refinement equation; in particular, we use the Fredholm
determinant theory to derive numerical estimates for the
spectral radius of these operators in certain spaces. This
new technique is particularly useful for estimating the
regularity in the cases where the refinement equation has an
infinite number of nonzero coefficients and in the
multidimensional cases.},
Doi = {10.4171/RMI/207},
Key = {fds287141}
}

@article{fds287139,
Author = {Daubechies, I and Huang, Y},
Title = {How does truncation of the mask affect a refinable
function?},
Journal = {Constructive Approximation},
Volume = {11},
Number = {3},
Pages = {365-380},
Publisher = {Springer Nature},
Year = {1995},
Month = {September},
ISSN = {0176-4276},
url = {http://dx.doi.org/10.1007/BF01208560},
Abstract = {If the mask of a refinable function has infinitely many
coefficients, or if the coefficients are irrational, then it
is often replaced by a finite mask with coefficients with
terminating decimal expansions when it comes to
applications. This note studies how such truncation affects
the refinable function. © 1995 Springer-Verlag New York,
Inc.},
Doi = {10.1007/BF01208560},
Key = {fds287139}
}

@article{fds316148,
Author = {Friedlander, S and Birman, JS and Daubechies, I},
Title = {A celebration or women in mathematics},
Journal = {Notices of the American Mathematical Society},
Volume = {42},
Number = {1},
Pages = {32-42},
Year = {1995},
Month = {January},
ISSN = {0002-9920},
Key = {fds316148}
}

@article{fds287137,
Author = {Daubechies, I and Huang, Y},
Title = {A decay theorem for refinable functions},
Journal = {Applied Mathematics Letters},
Volume = {7},
Number = {4},
Pages = {1-4},
Publisher = {Elsevier BV},
Year = {1994},
Month = {January},
ISSN = {0893-9659},
url = {http://dx.doi.org/10.1016/0893-9659(94)90001-9},
Abstract = {We show that a refinable function with absolutely summable
mask cannot have exponential decay in both time and
Doi = {10.1016/0893-9659(94)90001-9},
Key = {fds287137}
}

@article{fds315773,
Author = {Daubechies, I and Landau, HJ and Landau, Z},
Title = {Gabor Time-Frequency Lattices and the Wexler-Raz
Identity},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {1},
Number = {4},
Pages = {437-478},
Publisher = {Springer Nature},
Year = {1994},
Month = {January},
ISSN = {1069-5869},
url = {http://dx.doi.org/10.1007/s00041-001-4018-3},
Abstract = {Gabor time-frequency lattices are sets of functions of the
form (Formula presented.) generated from a given function
(Formula presented.) by discrete translations in time and
frequency. They are potential tools for the decomposition
and handling of signals that, like speech or music, seem
over short intervals to have well-defined frequencies that,
however, change with time. It was recently observed that the
behavior of a lattice (Formula presented.) can be connected
to that of a dual lattice (Formula presented.) Here we
establish this interesting relationship and study its
properties. We then clarify the results by applying the
theory of von Neumann algebras. One outcome is a simple
proof that for (Formula presented.) to span (Formula
presented.) the lattice (Formula presented.) must have at
least unit density. Finally, we exploit the connection
between the two lattices to construct expansions having
improved convergence and localization properties. © 1994,
Doi = {10.1007/s00041-001-4018-3},
Key = {fds315773}
}

@article{fds325015,
Author = {Daubechies, I},
Title = {Two Recent Results on Wavelets: Wavelet Bases for the
Interval, and Biorthogonal Wavelets Diagonalizing the
Derivative Operator},
Journal = {Wavelet Analysis and Its Applications},
Volume = {3},
Number = {C},
Pages = {237-257},
Year = {1994},
Month = {January},
url = {http://dx.doi.org/10.1016/B978-0-12-632370-2.50013-1},
Abstract = {The following two questions are often asked by researchers
interested in applying wavelet bases to concrete numerical
problems: 1) how does one adapt a wavelet basis on IR to a
wavelet basis on an interval without terrible edge effects?
2) how does the wavelet transform deal with the derivative
operator? This paper reviews several answers to each of
these questions, including some recent constructions and
Doi = {10.1016/B978-0-12-632370-2.50013-1},
Key = {fds325015}
}

@article{fds287136,
Author = {Daubechies, I},
Title = {Two Theorems on Lattice Expansions},
Journal = {Ieee Transactions on Information Theory},
Volume = {39},
Number = {1},
Pages = {3-6},
Year = {1993},
Month = {January},
url = {http://dx.doi.org/10.1109/18.179336},
Abstract = {It is shown that there is a trade-off between the smoothness
and decay properties of the dual functions, occurring in the
lattice expansion problem. More precisely, it is shown that
if g and [formula Omitted] are dual, then 1) at least one of
H<sup>1/2</sup>g and [formula Omitted] is not in [formula
Omitted] at least one of Hg and [formula Omitted] is not in
[formula Omitted]. Here, H is the operator-1/(4π<sup>2</sup>)d<sup>2</sup>/(dt<sup>2</sup>)
+ t<sup>2</sup>. The first result is a generalization of a
theorem first stated by Balian and independently by Low,
which was recently rigorously proved by Coifman and Semmes;
a new, much shorter proof was very recently given by Battle.
Battle suggests a theorem of type (i), but our result is
stronger in the sense that certain implicit assumptions made
by Battle are removed. Result 2) is new and relies heavily
on the fact that, when G E W<sup>2,2</sup>(S) with [formula
Omited] and G(0) = 0, then [formula Omitted]. The latter
result was not known to us and may be of independent
Doi = {10.1109/18.179336},
Key = {fds287136}
}

@article{fds287138,
Author = {Cohen, A and Daubechies, I and Vial, P},
Title = {Wavelets on the interval and fast wavelet
transforms},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {1},
Number = {1},
Pages = {54-81},
Publisher = {Elsevier BV},
Year = {1993},
Month = {January},
url = {http://dx.doi.org/10.1006/acha.1993.1005},
Abstract = {We discuss several constructions of orthonormal wavelet
bases on the interval, and we introduce a new construction
that avoids some of the disadvantages of earlier
Doi = {10.1006/acha.1993.1005},
Key = {fds287138}
}

@article{fds287132,
Author = {Daubechies, I and Lagarias, JC},
Title = {Sets of matrices all infinite products of which
converge},
Journal = {Linear Algebra and Its Applications},
Volume = {161},
Number = {C},
Pages = {227-263},
Year = {1992},
Month = {January},
ISSN = {0024-3795},
url = {http://dx.doi.org/10.1016/0024-3795(92)90012-Y},
Abstract = {An infinite product ∏∞i=1Mi of matrices converges (on
the right) if limi→∞ M1 ... Mi exists. A set
∑={Ai:i≥1}of n x n matrices is called an RCP set (right-
convergent product set) if all infinite products with each
element drawn from ∑ converge. Such sets of matrices arise
in constructing self-similar objects like von Koch's
snowflake curve, in various interpolation schemes, in
constructing wavelets of compact support, and in studying
nonhomogeneous Markov chains. This paper gives necessary
conditions and also some sufficient conditions for a set ∑
to be an RCP set. These are conditions on the eigenvalues
and left eigenspaces of matrices in ∑ and finite products
of these matrices. Necessary and sufficient conditions are
given for a finite set ∑ to be an RCP set having a limit
which is a continuous function on the space of all sequences
d with the sequence topology. Finite RCP sets of
column-stochastic matrices are completely characterized.
Some results are given on the problem of algorithmically
deciding if a given set ∑ is an RCP set. ©
1992.},
Doi = {10.1016/0024-3795(92)90012-Y},
Key = {fds287132}
}

@article{fds287135,
Author = {Antonini, M and Barlaud, M and Mathieu, P and Daubechies,
I},
Title = {Image coding using wavelet transform.},
Journal = {Ieee Transactions on Image Processing : a Publication of the
Ieee Signal Processing Society},
Volume = {1},
Number = {2},
Pages = {205-220},
Year = {1992},
Month = {January},
ISSN = {1057-7149},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18296155},
Abstract = {A scheme for image compression that takes into account
psychovisual features both in the space and frequency
domains is proposed. This method involves two steps. First,
a wavelet transform used in order to obtain a set of
biorthogonal subclasses of images: the original image is
decomposed at different scales using a pyramidal algorithm
architecture. The decomposition is along the vertical and
horizontal directions and maintains constant the number of
pixels required to describe the image. Second, according to
Shannon's rate distortion theory, the wavelet coefficients
are vector quantized using a multiresolution codebook. To
encode the wavelet coefficients, a noise shaping bit
allocation procedure which assumes that details at high
resolution are less visible to the human eye is proposed. In
order to allow the receiver to recognize a picture as
quickly as possible at minimum cost, a progressive
transmission scheme is presented. It is shown that the
wavelet transform is particularly well adapted to
progressive transmission.},
Doi = {10.1109/83.136597},
Key = {fds287135}
}

@article{fds318288,
Author = {Cohen, A and Daubechies, I and Feauveau, J},
Title = {Biorthogonal bases of compactly supported
wavelets},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {45},
Number = {5},
Pages = {485-560},
Publisher = {WILEY},
Year = {1992},
Month = {January},
url = {http://dx.doi.org/10.1002/cpa.3160450502},
Abstract = {Orthonormal bases of compactly supported wavelet bases
correspond to subband coding schemes with exact
reconstruction in which the analysis and synthesis filters
coincide. We show here that under fairly general conditions,
exact reconstruction schemes with synthesis filters
different from the analysis filters give rise to two dual
Riesz bases of compactly supported wavelets. We give
necessary and sufficient conditions for biorthogonality of
the corresponding scaling functions, and we present a
sufficient conditions for the decay of their Fourier
transforms. We study the regularity of these biorthogonal
bases. We provide several families of examples, all
symmetric (corresponding to “linear phase” filters). In
particular we can construct symmetric biorthogonal wavelet
bases with arbitraily high preassigned regularity; we also
show how to construct symmetric biorthogonal wavelet bases
“close” to a (nonsymmetric) orthonormal basis. Copyright
© 1992 Wiley Periodicals, Inc., A Wiley
Company},
Doi = {10.1002/cpa.3160450502},
Key = {fds318288}
}

@article{fds330517,
Author = {Moayeri, N and Daubechies, I and Song, Q and Wang,
HS},
Title = {Wavelet transform image coding using trellis coded vector
quantization},
Journal = {2015 Ieee International Conference on Acoustics, Speech, and
Signal Processing (Icassp)},
Volume = {4},
Pages = {405-408},
Publisher = {IEEE},
Year = {1992},
Month = {January},
ISBN = {0780305329},
url = {http://dx.doi.org/10.1109/ICASSP.1992.226350},
Abstract = {© 1992 IEEE. A combination of trellis coded quantization
(TCQ) and its vector alphabet generalization TCVQ is used to
code the coefficients resulting from a biorthogonal wavelet
transform in an image. TCVQ is a vector trellis coder with
fixed rate, very good rate-distortion performance, and yet
reasonable implementation complexity. The experimental
results show that the Lena image can be coded by this coding
system at the rate of 0.265 bpp to yield a peak
signal-to-noise ratio (PSNR) of about 29 dB. This PSNR is
about 3 dB larger than that obtained by a coding system of
the same rate that uses VQ to obtain the wavelet transform
coefficients. Naturally, the performance of the TCQ/TCVQ
wavelet transform coder can be improved if entropy-coded TCQ
and TCVQ coders are employed.},
Doi = {10.1109/ICASSP.1992.226350},
Key = {fds330517}
}

@article{fds317217,
Author = {Cohen, A and Daubechies, I},
Title = {A stability criterion for biorthogonal wavelet bases and
their related subband coding scheme},
Journal = {Duke Mathematical Journal},
Volume = {68},
Number = {2},
Pages = {313-335},
Publisher = {Duke University Press},
Year = {1992},
Month = {January},
ISSN = {0012-7094},
url = {http://dx.doi.org/10.1215/S0012-7094-92-06814-1},
Doi = {10.1215/S0012-7094-92-06814-1},
Key = {fds317217}
}

@article{fds287133,
Author = {Antonini, M and Barlaud, M and Mathieu, P and Daubechies,
I},
Title = {Image coding using vector quantization in the wavelet
transform domain},
Journal = {Icassp, Ieee International Conference on Acoustics, Speech
and Signal Processing Proceedings},
Volume = {4},
Pages = {2297-2300},
Publisher = {IEEE},
Year = {1990},
Month = {December},
url = {http://dx.doi.org/10.1109/icassp.1990.116036},
Abstract = {A two-step scheme for image compression that takes into
account psychovisual features in space and frequency domains
is proposed. A wavelet transform is first used in order to
obtain a set of orthonormal subclasses of images; the
original image is decomposed at different scales using a
pyramidal algorithm architecture. The decomposition is along
the vertical and horizontal directions and maintains the
number of pixels required to describe the image at a
constant. Second, according to Shannon's rate-distortion
theory, the wavelet coefficients are vector quantized using
a multiresolution codebook. To encode the wavelet
coefficients, a noise-shaping bit-allocation procedure which
assumes that details at high resolution are less visible to
the human eye is proposed. In order to allow the receiver to
recognize a picture as quickly as possible at minimum cost,
a progressive transmission scheme is presented. The wavelet
transform is particularly well adapted to progressive
transmission.},
Doi = {10.1109/icassp.1990.116036},
Key = {fds287133}
}

@article{fds287134,
Author = {Daubechies, I},
Title = {The Wavelet Transform, Time-Frequency Localization and
Signal Analysis},
Journal = {Ieee Transactions on Information Theory},
Volume = {36},
Number = {5},
Pages = {961-1005},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1990},
Month = {January},
url = {http://dx.doi.org/10.1109/18.57199},
Abstract = {Two different procedures are studied by which a frequency
analysis of a time-dependent signal can be effected, locally
in time. The first procedure is the short-time or windowed
Fourier transform, the second is the “wavelet
transform,” in which high frequency components are studied
with sharper time resolution than low frequency components.
The similarities and the differences between these two
methods are discussed. For both schemes a detailed study is
made of the reconstruction method and its stability, as a
function of the chosen time-frequency density. Finally the
notion of “time-frequency localization” is made precise,
within this framework, by two localization theorems. © 1990
IEEE},
Doi = {10.1109/18.57199},
Key = {fds287134}
}

@article{fds287131,
Author = {Daubechies, I},
Title = {Wavelets: A tool for time-frequency analysis},
Pages = {98},
Year = {1989},
Month = {December},
Abstract = {Summary form only given. In the simplest case, a family
wavelets is generated by dilating and translating a single
function of one variable: ha,b(x) = |a|-1/2h (x-b/a). The
parameters a and b may vary continuously, or be restricted
to a discrete lattice of values a = a0m, b = na0mb0. If the
dilation and translation steps a0 and b0 are not too large,
then any L2-function can be completely characterized by its
inner products with the elements of such a discrete lattice
of wavelets. Moreover, one can construct numerically stable
algorithms for the reconstruction of a function from these
inner products (the wavelet coefficients). For special
choices of the wavelet h decomposition and reconstruction
can be done very fast, via a tree algorithm. The wavelet
coefficients of a function give a time-frequency
decomposition of the function, with higher time-resolution
for high-frequency than for low-frequency components. The
analysis can easily be extended to higher dimensions. An
especially important case is orthonormal bases of wavelets.
It turns out that there exist functions h, with very good
regularity and decay properties, such that the discrete
lattice with a0 = 2 and b = 1 leads to an orthonormal set of
functions hmn that spans all of L2(R). Such orthonormal
bases are always associated with efficient tree
algorithms.},
Key = {fds287131}
}

@article{fds287128,
Author = {Daubechies, I and Paul, T},
Title = {Time-frequency localisation operators-a geometric phase
space approach: II. The use of dilations},
Journal = {Inverse Problems},
Volume = {4},
Number = {3},
Pages = {661-680},
Publisher = {IOP Publishing},
Year = {1988},
Month = {December},
ISSN = {0266-5611},
url = {http://dx.doi.org/10.1088/0266-5611/4/3/009},
Abstract = {Operators which localise both in time and frequency are
constructed. They restrict to a finite time interval and cut
off low as well as high frequencies (band-pass filters).
Explicit expressions for eigenvalues and eigenfunctions
(Laguerre functions) are given.},
Doi = {10.1088/0266-5611/4/3/009},
Key = {fds287128}
}

@article{fds287129,
Author = {Daubechies, I},
Title = {Wavelet transform, time-frequency localization and signal
analysis},
Volume = {25 n 13},
Pages = {42},
Year = {1988},
Month = {December},
Abstract = {Summary form only given, as follows. Two different
procedures are studied by which a frequency analysis of a
time-dependent signal can be effected, locally in time. The
first procedure is the short-time or windowed Fourier
transform; the second is the wavelet transform, in which
high-frequency components are studied with sharper time
resolution than low-frequency components. The similarities
and the differences between these two methods are discussed.
For both schemes a detailed study is made of the
reconstruction method and its stability, as a function of
the chosen time-frequency density. Finally the notion of
time-frequency localization is made precise, within this
framework, by two localization theorems.},
Key = {fds287129}
}

@article{fds287130,
Author = {Daubechies, I},
Title = {Time-Frequency Localization Operators: A Geometric Phase
Space Approach},
Journal = {Ieee Transactions on Information Theory},
Volume = {34},
Number = {4},
Pages = {605-612},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1988},
Month = {January},
url = {http://dx.doi.org/10.1109/18.9761},
Abstract = {We define a set of operators which localize in both time and
frequency. These operators are similar to but different from
the low-pass time-limiting operators, the singular functions
of which are the prolate spheroidal wave functions. Our
construction differs from the usual approach in that we
treat the time-frequency plane as one geometric whole (phase
space) rather than as two separate spaces. For disk-shaped
or ellipse-shaped domains in the time-frequency plane, the
associated localization operators are remarkably simple.
Their eigenfunctions are Hermite functions, and the
corresponding eigenvalues are given by simple explicit
formulas involving the incomplete gamma functions. © 1988
IEEE},
Doi = {10.1109/18.9761},
Key = {fds287130}
}

@article{fds318289,
Author = {Daubechies, I},
Title = {Orthonormal bases of compactly supported
wavelets},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {41},
Number = {7},
Pages = {909-996},
Publisher = {WILEY},
Year = {1988},
Month = {January},
url = {http://dx.doi.org/10.1002/cpa.3160410705},
Abstract = {We construct orthonormal bases of compactly supported
wavelets, with arbitrarily high regularity. The order of
regularity increases linearly with the support width. We
start by reviewing the concept of multiresolution analysis
as well as several algorithms in vision decomposition and
reconstruction. The construction then follows from a
Wiley Periodicals, Inc., A Wiley Company},
Doi = {10.1002/cpa.3160410705},
Key = {fds318289}
}

@article{fds318290,
Author = {Daubechies, I and Grossmann, A},
Title = {Frames in the bargmann space of entire functions},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {41},
Number = {2},
Pages = {151-164},
Publisher = {WILEY},
Year = {1988},
Month = {January},
url = {http://dx.doi.org/10.1002/cpa.3160410203},
Abstract = {We look at the decomposition of arbitrary f in L2(R) in
terms of the family of functions φmn(x) = π−1/4exp{ −
1/2imnab + i max − 1/2(x − nb)2}, with a, b > 0. We
derive bounds and explicit formulas for the minimal
expansion coefficients in the case where ab = 2π/N, N an
integer ≧ 2. Transported to the Hilbert space F of entire
functions introduced by V. Bargmann, these results are
expressed as inequalities of the form We conjecture that
these inequalities remain true for all a, b such that ab <
Company},
Doi = {10.1002/cpa.3160410203},
Key = {fds318290}
}

@article{fds287127,
Author = {Daubechies, I and Klauder, JR and Paul, T},
Title = {Wiener measures for path integrals with affine kinematic
variables},
Journal = {Journal of Mathematical Physics},
Volume = {28},
Number = {1},
Pages = {85-102},
Publisher = {AIP Publishing},
Year = {1987},
Month = {January},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.527812},
Abstract = {The results obtained earlier have been generalized to show
that the path integral for the affine coherent state matrix
element of a unitary evolution operator exp(-iTH) can be
written as a well-defined Wiener integral, involving Wiener
measure on the Lobachevsky half-plane, in the limit that the
diffusion constant diverges. This approach works for a wide
class of Hamiltonians, including, e.g., -d2/dx2 + V(x) on
L2(ℝ +), with V sufficiently singular at x = 0. © 1987
American Institute of Physics.},
Doi = {10.1063/1.527812},
Key = {fds287127}
}

@article{fds287126,
Author = {Daubechies, I and Grossmann, A and Meyer, Y},
Title = {Painless nonorthogonal expansions},
Journal = {Journal of Mathematical Physics},
Volume = {27},
Number = {5},
Pages = {1271-1283},
Publisher = {AIP Publishing},
Year = {1986},
Month = {January},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.527388},
Abstract = {In a Hilbert spaced ℋ, discrete families of vectors {hj}
with the property that f = ∑j〈j|f〉h j for every f in
ℋ are considered. This expansion formula is obviously true
if the family is an orthonormal basis of ℋ, but also can
hold in situations where the hj are not mutually orthogonal
and are "overcomplete." The two classes of examples studied
here are (i) appropriate sets of Weyl-Heisenberg coherent
states, based on certain (non-Gaussian) fiducial vectors,
and (ii) analogous families of affine coherent states. It is
believed, that such "quasiorthogonal expansions" will be a
useful tool in many areas of theoretical physics and applied
mathematics. © 1966 American Institute of
Physics.},
Doi = {10.1063/1.527388},
Key = {fds287126}
}

@article{fds287125,
Author = {Daubechies, I and Klauder, JR},
Title = {Quantum-mechanical path integrals with Wiener measure for
all polynomial Hamiltonians. II},
Journal = {Journal of Mathematical Physics},
Volume = {26},
Number = {9},
Pages = {2239-2256},
Publisher = {AIP Publishing},
Year = {1985},
Month = {January},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.526803},
Abstract = {The coherent-state representation of quantum-mechanical
propagators as well-defined phase-space path integrals
involving Wiener measure on continuous phase-space paths in
the limit that the diffusion constant diverges is formulated
and proved. This construction covers a wide class of
self-adjoint Hamiltonians, including all those which are
polynomials in the Heisenberg operators; in fact, this
method also applies to maximal symmetric Hamiltonians that
do not possess a self-adjoint extension. This construction
also leads to a natural covariance of the path integral
under canonical transformations. An entirely parallel
discussion for spin variables leads to the representation of
the propagator for an arbitrary spin-operator Hamiltonian as
well-defined path integrals involving Wiener measure on the
unit sphere, again in the limit that the diffusion constant
diverges. © 1985 American Institute of Physics.},
Doi = {10.1063/1.526803},
Key = {fds287125}
}

@article{fds287124,
Author = {Daubechies, I},
Title = {One electron molecules with relativistic kinetic energy:
Properties of the discrete spectrum},
Journal = {Communications in Mathematical Physics},
Volume = {94},
Number = {4},
Pages = {523-535},
Publisher = {Springer Nature},
Year = {1984},
Month = {December},
ISSN = {0010-3616},
url = {http://dx.doi.org/10.1007/BF01403885},
Abstract = {We discuss the discrete spectrum of the operator
{Mathematical expression}. More specifically, we study 1)
the behaviour of the eigenvalues when the internuclear
distances contract, 2) the existence of a c-independent
lower bound for HK(c)-mc2, 3) the nonrelativistic limit of
the eigenvalues of HK(c)-mc2. © 1984 Springer-Verlag.},
Doi = {10.1007/BF01403885},
Key = {fds287124}
}

@article{fds287122,
Author = {Klauder, JR and Daubechies, I},
Title = {Quantum Mechanical Path Integrals with Wiener Measures for
all Polynomial Hamiltonians},
Journal = {Physical Review Letters},
Volume = {52},
Number = {14},
Pages = {1161-1164},
Publisher = {American Physical Society (APS)},
Year = {1984},
Month = {January},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.52.1161},
Abstract = {We construct arbitrary matrix elements of the quantum
evolution operator for a wide class of self-adjoint
canonical Hamiltonians, including those which are polynomial
in the Heisenberg operators, as the limit of well defined
path integrals involving Wiener measure on phase space, as
the diffusion constant diverges. A related construction
achieves a similar result for an arbitrary spin Hamiltonian.
© 1984 The American Physical Society.},
Doi = {10.1103/PhysRevLett.52.1161},
Key = {fds287122}
}

@article{fds287123,
Author = {Daubechies, I and Lieb, EH},
Title = {Relativistic Molecules with Coulomb Interaction},
Journal = {North-Holland Mathematics Studies},
Volume = {92},
Number = {C},
Pages = {143-148},
Publisher = {Elsevier},
Year = {1984},
Month = {January},
ISSN = {0304-0208},
url = {http://dx.doi.org/10.1016/S0304-0208(08)73689-2},
Abstract = {As an approximation to a relativistic one-electron molecule,
we study the operator, with Zj≥ 0 for all j. H is bounded
below iff for all j. Under this condition, we show that 1)
The system is stable when the nuclear repulsion is taken
into account, i.e., where E0 inf spec H.2) the ground state
energy E0is an increasing function of the internuclear
distances | Rj- Rk. © 1984, Elsevier Science & Technology.
Doi = {10.1016/S0304-0208(08)73689-2},
Key = {fds287123}
}

@article{fds287119,
Author = {Daubechies, I},
Title = {An uncertainty principle for fermions with generalized
kinetic energy},
Journal = {Communications in Mathematical Physics},
Volume = {90},
Number = {4},
Pages = {511-520},
Publisher = {Springer Nature},
Year = {1983},
Month = {December},
ISSN = {0010-3616},
url = {http://dx.doi.org/10.1007/BF01216182},
Abstract = {We derive semiclassical upper bounds for the number of bound
states and the sum of negative eigenvalues of the
one-particle Hamiltonians h=f(-i∇)+V(x) acting on
L2(ℝn). These bounds are then used to derive a lower bound
on the kinetic energy {Mathematical expression} for an
N-fermion wavefunction ψ. We discuss two examples in more
detail:f(p)=|p| and f(p)=(p2+m2)1/2-m, both in three
Doi = {10.1007/BF01216182},
Key = {fds287119}
}

@article{fds287120,
Author = {Daubechies, I and Lieb, EH},
Title = {One-electron relativistic molecules with Coulomb
interaction},
Journal = {Communications in Mathematical Physics},
Volume = {90},
Number = {4},
Pages = {497-510},
Publisher = {Springer Nature},
Year = {1983},
Month = {December},
ISSN = {0010-3616},
url = {http://dx.doi.org/10.1007/BF01216181},
Abstract = {As an approximation to a relativistic one-electron molecule,
we study the operator {Mathematical expression} with Zj≧0,
e-2=137.04. H is bounded below if and only if e2Zj≦2/π
all j. Assuming this condition, the system is unstable when
e2∑Zj>2/π in the sense that E0=inf spec(H)→-∞ as the
Rj→0, all j. We prove that the nuclear Coulomb repulsion
more than restores stability; namely {Mathematical
expression}. We also show that E0 is an increasing function
of the internuclear distances |Ri-Rj|. © 1983
Springer-Verlag.},
Doi = {10.1007/BF01216181},
Key = {fds287120}
}

@article{fds287121,
Author = {Daubechies, I and Klauder, JR},
Title = {Measures for more quadratic path integrals},
Journal = {Letters in Mathematical Physics},
Volume = {7},
Number = {3},
Pages = {229-234},
Publisher = {Springer Nature America, Inc},
Year = {1983},
Month = {May},
ISSN = {0377-9017},
url = {http://dx.doi.org/10.1007/BF00400438},
Abstract = {We show that the coherent state matrix elements of the
quantum mechanical propagator for all quadratic Hamiltonians
may be represented as the limit of path integrals with
respect to appropriately modified Wiener measures as the
associated diffusion constant tends to infinity. © 1983 D.
Reidel Publishing Company.},
Doi = {10.1007/BF00400438},
Key = {fds287121}
}

@article{fds287116,
Author = {Daubechies, I},
Title = {Continuity statements and counterintuitive examples in
connection with Weyl quantization},
Journal = {Journal of Mathematical Physics},
Volume = {24},
Number = {6},
Pages = {1453-1461},
Publisher = {AIP Publishing},
Year = {1982},
Month = {December},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.525882},
Abstract = {We use the properties of an integral transform relating a
classical function f with the matrix elements between
coherent states of its quantal counterpart Q f, to derive
continuity properties of the Weyl transform from classes of
distributions to classes of quadratic forms. We also give
examples of pathological behavior of the Weyl transform with
respect to other topologies (e.g., bounded functions leading
to unbounded operators). © 1983 American Institute of
Physics.},
Doi = {10.1063/1.525882},
Key = {fds287116}
}

@article{fds287117,
Author = {Daubechies, I and Grossmann, A and Reignier, J},
Title = {An integral transform related to quantization. II. Some
mathematical properties},
Journal = {Journal of Mathematical Physics},
Volume = {24},
Number = {2},
Pages = {239-254},
Publisher = {AIP Publishing},
Year = {1982},
Month = {December},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.525699},
Abstract = {We study in more detail the mathematical properties of the
integral transform relating the matrix elements between
coherent states of a quantum operator to the corresponding
classical function. Explicit families of Hilbert spaces are
constructed between which the integral transform is an
isomorphism. © 1983 American Institute of
Physics.},
Doi = {10.1063/1.525699},
Key = {fds287117}
}

@article{fds287118,
Author = {Klauder, JR and Daubechies, I},
Title = {Measures for path integrals},
Journal = {Physical Review Letters},
Volume = {48},
Number = {3},
Pages = {117-120},
Year = {1982},
Month = {January},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.48.117},
Abstract = {By exploitation of the overcompleteness of coherent states
expressions are presented for path integrals in terms of
genuine (Wiener) path-space measures for driven harmonic
oscillators which when projected onto the subspace spanned
by coherent-state matrix elements yield the appropriate
quantum mechanical propagator. © 1982 The American Physical
Society.},
Doi = {10.1103/PhysRevLett.48.117},
Key = {fds287118}
}

@article{fds287115,
Author = {Daubechies, I and Klauder, JR},
Title = {Constructing measures for path integrals},
Journal = {Journal of Mathematical Physics},
Volume = {23},
Number = {10},
Pages = {1806-1822},
Publisher = {AIP Publishing},
Year = {1981},
Month = {December},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.525234},
Abstract = {The overcompleteness of the coherent states for the
Heisenberg-Weyl group implies that many different integral
kernels can be used to represent the same operator. Within
such an equivalence class we construct an integral kernel to
represent the quantum-mechanical evolution operator for
certain dynamical systems in the form of a path integral
that involves genuine (Wiener) measures on continuous
phase-space paths. To achieve this goal it is necessary to
employ an expression for the classical action different from
the usual one. © 1982 American Institute of
Physics.},
Doi = {10.1063/1.525234},
Key = {fds287115}
}

@article{fds287114,
Author = {Daubechies, I},
Title = {On the distributions corresponding to bounded operators in
the Weyl quantization},
Journal = {Communications in Mathematical Physics},
Volume = {75},
Number = {3},
Pages = {229-238},
Publisher = {Springer Nature},
Year = {1980},
Month = {October},
ISSN = {0010-3616},
url = {http://dx.doi.org/10.1007/BF01212710},
Abstract = {Using properties of an integral transform giving directly
the matrix elements of a quantum mechanical operator from
the corresponding classical function, we restrict the class
of distributions corresponding to bounded operators. As a
consequence, we can exhibit a class of functions yielding
trace-class operators, and give a bound on their trace-norm.
Doi = {10.1007/BF01212710},
Key = {fds287114}
}

@article{fds287113,
Author = {Daubechies, I and Grossmann, A},
Title = {An integral transform related to quantization},
Journal = {Journal of Mathematical Physics},
Volume = {21},
Number = {8},
Pages = {2080-2090},
Publisher = {AIP Publishing},
Year = {1979},
Month = {December},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.524702},
Abstract = {We study in some detail the correspondence between a
function f on phase space and the matrix elements (Qf)(a, b)
of its quantized Q f between the coherent states |a< and
|b<. It is an integral transform: Qf(a, b) = ∫{a, b |v}
f(v) dv which resembles in many ways the integral transform
of Bargmann. We obtain the matrix elements of Q f between
harmonic oscillator states as the Fourier coefficients of f
with respect to an explicit orthonormal system. © 1980
American Institute of Physics.},
Doi = {10.1063/1.524702},
Key = {fds287113}
}

@article{fds287110,
Author = {Aerts, D and Daubechies, I},
Title = {A characterization of subsystems in physics},
Journal = {Letters in Mathematical Physics},
Volume = {3},
Number = {1},
Pages = {11-17},
Publisher = {Springer Nature},
Year = {1979},
Month = {January},
ISSN = {0377-9017},
url = {http://dx.doi.org/10.1007/BF00959533},
Abstract = {Working within the framework of the propositional system
formalism, we use a previous study [1] of the description of
two independent physical systems as one big physical system
to derive a characterization of a (non-interacting) physical
subsystem. We discuss the classical case and the quantum
case. © 1979 D. Reidel Publishing Company.},
Doi = {10.1007/BF00959533},
Key = {fds287110}
}

@article{fds287112,
Author = {Aerts, D and Daubechies, I},
Title = {A mathematical condition for a sublattice of a propositional
system to represent a physical subsystem, with a physical
interpretation},
Journal = {Letters in Mathematical Physics},
Volume = {3},
Number = {1},
Pages = {19-27},
Publisher = {Springer Nature},
Year = {1979},
Month = {January},
ISSN = {0377-9017},
url = {http://dx.doi.org/10.1007/BF00959534},
Abstract = {We display three equivalent conditions for a sublattice,
isomorphic to a P {Mathematical expression}, of the
propositional system P(ℋ) of a quantum system to be the
representation of a physical subsystem (see [1]). These
conditions are valid for dim {Mathematical expression}≥3.
We prove that one of them is still necessary and sufficient
if dim {Mathematical expression}<3. A physical
interpretation of this condition is given. © 1979 D. Reidel
Publishing Company.},
Doi = {10.1007/BF00959534},
Key = {fds287112}
}

@article{fds287111,
Author = {Daubechies, I},
Title = {An application of hyperdifferential operators to holomorphic
quantization},
Journal = {Letters in Mathematical Physics},
Volume = {2},
Number = {6},
Pages = {459-469},
Publisher = {Springer Nature America, Inc},
Year = {1978},
Month = {November},
ISSN = {0377-9017},
url = {http://dx.doi.org/10.1007/BF00398498},
Abstract = {We use a hyperdifferential operator approach to study
holomorphic quantization. We explicitly construct the
Hilbert space operator which corresponds to a given
holomorphic function. We further construct the adjoint and
products of such operators and we discuss some special cases
Company.},
Doi = {10.1007/BF00398498},
Key = {fds287111}
}



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