%% Papers Published
@article{fds363771,
Author = {Stefanov, P and Zhong, Y},
Title = {INVERSE BOUNDARY PROBLEM FOR THE TWO PHOTON ABSORPTION
TRANSPORT EQUATION},
Journal = {Siam Journal on Mathematical Analysis},
Volume = {54},
Number = {3},
Pages = {2753-2767},
Year = {2022},
Month = {January},
url = {http://dx.doi.org/10.1137/21M1417387},
Abstract = {We study the inverse boundary problem for the nonlinear two
photon absorption radiative transport equation. We show that
the absorption coefficients and the scattering coefficient
can be uniquely determined from the albedo operator. If the
scattering is absent, we do not require smallness of the
incoming source, and the reconstruction of the absorption
coefficients is explicit.},
Doi = {10.1137/21M1417387},
Key = {fds363771}
}
@article{fds356127,
Author = {Zhao, H and Zhong, Y},
Title = {Quantitative PAT with simplified P N
approximation},
Journal = {Inverse Problems},
Volume = {37},
Number = {5},
Year = {2021},
Month = {May},
url = {http://dx.doi.org/10.1088/1361-6420/abf318},
Abstract = {The photoacoustic tomography (PAT) is a hybrid modality that
combines the optics and acoustics to obtain high resolution
and high contrast imaging of heterogeneous media. In this
work, our objective is to study the inverse problem in the
quantitative step of PAT which aims to reconstruct the
optical coefficients of the governing radiative transport
equation from the ultrasound measurements. In our analysis,
we take the simplified P N approximation of the radiative
transport equation as the physical model and then show the
uniqueness and stability for this modified inverse problem.
Numerical simulations based on synthetic data are presented
to validate our analysis.},
Doi = {10.1088/1361-6420/abf318},
Key = {fds356127}
}
@article{fds361357,
Author = {Li, W and Schotland, JC and Yang, Y and Zhong, Y},
Title = {An Acousto-electric Inverse Source Problem},
Journal = {Siam Journal on Imaging Sciences},
Volume = {14},
Number = {4},
Pages = {1601-1616},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2021},
Month = {January},
url = {http://dx.doi.org/10.1137/21m1406568},
Doi = {10.1137/21m1406568},
Key = {fds361357}
}
@article{fds360503,
Author = {Zhong, Y and Zhao, H and Ren, K},
Title = {Separability of the kernel function in an integral
formulation for anisotropic radiative transfer
equation},
Journal = {Siam Journal on Mathematical Analysis},
Volume = {53},
Number = {5},
Pages = {5613-5613},
Publisher = {Society for Industrial and Applied Mathematics},
Year = {2021},
Key = {fds360503}
}
@article{fds353471,
Author = {Zhong, Y and Zhao, H},
Title = {A Fast Algorithm for Time-Dependent Radiative Transport
Equation Based on Integral Formulation},
Journal = {Csiam Transactions on Applied Mathematics},
Volume = {1},
Number = {2},
Pages = {346-364},
Publisher = {Global Science Press},
Year = {2020},
Month = {June},
url = {http://dx.doi.org/10.4208/csiam-am.2020-0012},
Doi = {10.4208/csiam-am.2020-0012},
Key = {fds353471}
}
@article{fds353472,
Author = {Li, W and Yang, Y and Zhong, Y},
Title = {Inverse transport problem in fluorescence ultrasound
modulated optical tomography with angularly averaged
measurements},
Journal = {Inverse Problems},
Volume = {36},
Number = {2},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.1088/1361-6420/ab4609},
Abstract = {We consider an inverse transport problem in fluorescence
ultrasound modulated optical tomography (fUMOT) with
angularly averaged illuminations and measurements. We study
the uniqueness and stability of the reconstruction of the
absorption coefficient and the quantum efficiency of the
fluorescent probes. Reconstruction algorithms are proposed
and numerical validations are performed. This paper is an
extension of Li et al (2019 SIAM J. Appl. Math. 79 356-76),
where a diffusion model for this problem was
considered.},
Doi = {10.1088/1361-6420/ab4609},
Key = {fds353472}
}
@article{fds353473,
Author = {Ren, K and Zhang, R and Zhong, Y},
Title = {A fast algorithm for radiative transport in isotropic
media},
Journal = {Journal of Computational Physics},
Volume = {399},
Year = {2019},
Month = {December},
url = {http://dx.doi.org/10.1016/j.jcp.2019.108958},
Abstract = {Constructing efficient numerical solution methods for the
equation of radiative transfer (ERT) remains as a
challenging task in scientific computing despite of the
tremendous development on the subject in recent years. We
present in this work a simple fast computational algorithm
for solving the ERT in isotropic media. The algorithm we
developed has two steps. In the first step, we solve a
volume integral equation for the angularly-averaged ERT
solution using iterative schemes such as the GMRES method.
The computation in this step is accelerated with a fast
multipole method (FMM). In the second step, we solve a
scattering-free transport equation to recover the angular
dependence of the ERT solution. The algorithm does not
require the underlying medium be homogeneous. We present
numerical simulations under various scenarios to demonstrate
the performance of the proposed numerical algorithm for both
homogeneous and heterogeneous media.},
Doi = {10.1016/j.jcp.2019.108958},
Key = {fds353473}
}
@article{fds353474,
Author = {Ren, K and Zhong, Y},
Title = {Imaging point sources in heterogeneous environments},
Journal = {Inverse Problems},
Volume = {35},
Number = {12},
Year = {2019},
Month = {October},
url = {http://dx.doi.org/10.1088/1361-6420/ab3497},
Abstract = {Imaging point sources in heterogeneous environments from
boundary or far-field measurements has been extensively
studied in the past. In most existing results, the
environment, represented by the refractive index function in
the model equation, is assumed known in the imaging process.
In this work, we investigate the impact of environment
uncertainty on the reconstruction of point sources inside
it. Following the techniques developed by El Badia and El
Hajj (2012 C. R. Acad. Sci. Paris I 350 1031-5), we derive
stability of reconstructing point sources in heterogeneous
media with respect to measurement error as well as smooth
changes in the environment, that is, the refractive index.
Numerical simulations with synthetic data are presented to
further explore the derived stability properties.},
Doi = {10.1088/1361-6420/ab3497},
Key = {fds353474}
}
@article{fds353475,
Author = {Zhao, H and Zhong, Y},
Title = {A hybrid adaptive phase space method for reflection
traveltime tomography},
Journal = {Siam Journal on Imaging Sciences},
Volume = {12},
Number = {1},
Pages = {28-53},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18M117426X},
Abstract = {We present a hybrid imaging method for a challenging
traveltime tomography problem which includes both unknown
medium and unknown scatterers in a bounded domain. The goal
is to recover both the medium and the boundary of the
scatterers from the scattering relation data on the domain
boundary. Our method is composed of three steps: (1)
preprocess the data to classify them into three different
categories of measurements corresponding to nonbroken rays,
broken-once rays, and others, respectively, (2) use the the
nonbroken ray data and an effective data-driven layer
stripping strategy---an optimization based iterative imaging
method---to recover the medium velocity outside the convex
hull of the scatterers, and (3) use selected broken-once ray
data to recover the boundary of the scatterers---a direct
imaging method. By numerical tests, we show that our hybrid
method can recover both the unknown medium and the
not-too-concave scatterers efficiently and
robustly.},
Doi = {10.1137/18M117426X},
Key = {fds353475}
}
@article{fds353476,
Author = {Bryson, J and Zhao, H and Zhong, Y},
Title = {Intrinsic complexity and scaling laws: From random fields to
random vectors},
Journal = {Multiscale Modeling & Simulation},
Volume = {17},
Number = {1},
Pages = {460-481},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18M1187908},
Abstract = {Random fields are commonly used for modeling of spatially
(or timely) dependent stochastic processes. In this study,
we provide a characterization of the intrinsic complexity of
a random field in terms of its second order statistics,
e.g., the covariance function, based on the Karhumen Loeve
expansion. We then show scaling laws for the intrinsic
complexity of a random field in terms of the correlation
length as it goes to 0. In the discrete setting, the analogy
is approximation of a set of random vectors based on
principal component analysis. We provide a precise scaling
law when the random vectors have independent and identically
distributed entries using random matrix theory as well as
when the random vectors have a specific covariance
structure.},
Doi = {10.1137/18M1187908},
Key = {fds353476}
}
@article{fds353477,
Author = {Li, W and Yang, Y and Zhong, Y},
Title = {A hybrid inverse problem in the fluorescence ultrasound
modulated optical tomography in the diffusive
regime},
Journal = {Siam Journal on Applied Mathematics},
Volume = {79},
Number = {1},
Pages = {356-376},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18M117889X},
Abstract = {We investigate a hybrid inverse problem in fluorescence
ultrasound modulated optical tomography in the diffusive
regime. We prove that the boundary measurement of the photon
currents allows unique and stable reconstructions of the
absorption coefficient of the fluorophores at the excitation
frequency and the quantum efficiency coefficient
simultaneously, provided that some background medium
parameters are known. Reconstruction algorithms are proposed
and numerically implemented as well.},
Doi = {10.1137/18M117889X},
Key = {fds353477}
}
@article{fds353478,
Author = {Zhao, H and Zhong, Y},
Title = {Instability of an Inverse Problem for the Stationary
Radiative Transport Near the Diffusion Limit},
Journal = {Siam Journal on Mathematical Analysis},
Volume = {51},
Number = {5},
Pages = {3750-3768},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18m1222582},
Doi = {10.1137/18m1222582},
Key = {fds353478}
}
@article{fds353479,
Author = {Zhong, Y and Ren, K and Tsai, R},
Title = {An implicit boundary integral method for computing electric
potential of macromolecules in solvent},
Journal = {Journal of Computational Physics},
Volume = {359},
Pages = {199-215},
Year = {2018},
Month = {April},
url = {http://dx.doi.org/10.1016/j.jcp.2018.01.021},
Abstract = {A numerical method using implicit surface representations is
proposed to solve the linearized Poisson–Boltzmann
equation that arises in mathematical models for the
electrostatics of molecules in solvent. The proposed method
uses an implicit boundary integral formulation to derive a
linear system defined on Cartesian nodes in a narrowband
surrounding the closed surface that separates the molecule
and the solvent. The needed implicit surface is constructed
from the given atomic description of the molecules, by a
sequence of standard level set algorithms. A fast multipole
method is applied to accelerate the solution of the linear
system. A few numerical studies involving some standard test
cases are presented and compared to other existing
results.},
Doi = {10.1016/j.jcp.2018.01.021},
Key = {fds353479}
}
@article{fds353480,
Author = {Ren, K and Zhang, R and Zhong, Y},
Title = {Inverse transport problems in quantitative PAT for molecular
imaging},
Journal = {Inverse Problems},
Volume = {31},
Number = {12},
Year = {2015},
Month = {November},
url = {http://dx.doi.org/10.1088/0266-5611/31/12/125012},
Abstract = {Fluorescence photoacoustic tomography (fPAT) is a molecular
imaging modality that combines photoacoustic tomography with
fluorescence imaging to obtain high-resolution imaging of
fluorescence distributions inside heterogeneous media. The
objective of this work is to study inverse problems in the
quantitative step of fPAT where we intend to reconstruct
physical coefficients in a coupled system of radiative
transport equations using internal data recovered from
ultrasound measurements. We derive uniqueness and stability
results on the inverse problems and develop some efficient
algorithms for image reconstructions. Numerical simulations
based on synthetic data are presented to validate the
theoretical analysis. The results we present here complement
these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6
2024-49) on the same problem but in the diffusive
regime.},
Doi = {10.1088/0266-5611/31/12/125012},
Key = {fds353480}
}
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Mathematics Department