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Publications of William K. Allard    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds200674,
   Author = {W.K. Allard and Guanglian Chen and Mauro Maggioni},
   Title = {W.K. Allard, G. Chen, M. Maggioni Multiscale Geometric
             Methods for Data Sets II: Geometric Wavelets},
   Journal = {to appear in ACHA},
   Year = {2011},
   Key = {fds200674}
}

@article{fds243260,
   Author = {Allard, WK},
   Title = {Total variation for image denoising: III.
             Examples},
   Journal = {Siam Journal on Imaging Sciences},
   Volume = {2},
   Year = {2009},
   url = {http://www.math.duke.edu/~wka/new.pdf},
   Key = {fds243260}
}

@article{fds243261,
   Author = {Allard, WK},
   Title = {Total variation regularization for image denoising,
             geometric theory},
   Journal = {Siam Journal on Mathematical Analysis},
   Volume = {39},
   Number = {4},
   Pages = {1150-1190},
   Year = {2007},
   Month = {December},
   ISSN = {0036-1410},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000253016600006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {Let Ω be an open subset of ℝn, where 2 < n < 7; we assume
             n > 2 because the case n = 1 has been treated elsewhere (see
             [S. S. Alliney, IEEE Trans. Signal Process., 40 (1992), pp.
             1548-1562] and is quite different from the case n > 1; we
             assume n ≤ 7 because we will make use of the regularity
             theory for area minimizing hypersurfaces. Let ℱ(Ω.) = {f
             ∈ L1 (Ω)∩lL∞(Ω) : f ≥ 0} Suppose s ∈ ℱ(Ω) and
             γ : ℝ → [0, ∞) is locally Lipschitzian, positive on
             ℝ ∼ {0}, and zero at zero. Let F(f) = ∫Ω γ(f(x) -
             s(x)) dℒn x for f ∈ ℱ(Ω); here ℒn is Lebesgue
             measure on ℝn. Note that F(f) = 0 if and only if f(x)
             -s(x) for ℒn almost all x ∈ ℝn. In the denoising
             literature F would be called a fidelity in that it measures
             deviation from s, which could be a noisy grayscale image.
             Let ε > 0 and let F ε(f) = εTV(f) + F(f) for f ∈
             ℱ(Ω); here TV(f) is the total variation of f. A minimizer
             of Fε is called a total variation regularization of s.
             Rudin, Osher, and Fatemi and Chan and Esedoglu have studied
             total variation regularizations where γ(y) = y 2 and γ(y)
             = |y|, y ∈ ℝ, respectively. As these and other examples
             show, the geometry of a total variation regularization is
             quite sensitive to changes in γ. Let f be a total variation
             regularization of s. The first main result of this paper is
             that the reduced boundaries of the sets {f > y}, 0 < y <
             ∞, are embedded C1, μ hypersurfaces for any μ ∈ (0,1)
             where n > 2 and any μ ∈ (0,1] where n = 2; moreover, the
             generalized mean curvature of the sets {f ≥ y} will be
             bounded in terms of y, ε and the magnitude of |s| near the
             point in question. In fact, this result holds for a more
             general class of fidelities than those described above. A
             second result gives precise curvature information about the
             reduced boundary of {f > y} in regions where s is smooth,
             provided F is convex. This curvature information will allow
             us to construct a number of interesting examples of total
             variation regularizations in this and in a subsequent paper.
             In addition, a number of other theorems about
             regularizations are proved. © 2007 Society for Industrial
             and Applied Mathematics.},
   Doi = {10.1137/060662617},
   Key = {fds243261}
}

@article{fds243262,
   Author = {Allard, WK},
   Title = {Total variation regularization for image denoising: I.
             Geometric theory using total variation regularization; II
             Examples.},
   Journal = {Siam Journal on Mathematical Analysis},
   Volume = {39},
   Number = {4},
   Year = {2007},
   Month = {November},
   url = {http://www.math.duke.edu/~wka},
   Abstract = {http://www.math.duke.edu/~wka},
   Key = {fds243262}
}

@article{fds243263,
   Author = {Allard, WK},
   Title = {The reconstruction of surfaces in R3 by reflection},
   Journal = {The Journal of Geometric Analysis},
   Volume = {9},
   Number = {5},
   Year = {1999},
   url = {http://www.math.duke.edu/faculty/allard/papers/allabst.ps},
   Key = {fds243263}
}

@article{fds9254,
   Author = {William K Allard},
   Title = {An Introduction to the Deferred Execution
             Tool},
   Journal = {Proceedings of Ninth SIAM Annual Conference on Parallel
             Processing for Scientific Computing, (SIAM) March
             1999},
   Key = {fds9254}
}


%% Preprints   
@article{fds167778,
   Author = {W.K. Allard},
   Title = {A boundary approximation algorithm for planar
             domains},
   Year = {2009},
   url = {http://www.math.duke.edu/~wka/bdry.pdf},
   Key = {fds167778}
}

@article{fds9393,
   Author = {William K. Allard and John Trangenstein},
   Title = {On the Performance of a Distributed Object Oriented Adaptive
             Mesh Refinement Code},
   url = {http://www.math.duke.edu/~wka/papers/adaptive.ps},
   Key = {fds9393}
}

@article{fds9392,
   Author = {William K. Allard},
   Title = {Users Guide to the Deferred Execution Tool},
   url = {http://www.math.duke.edu/~wka/papers/deferred.ps},
   Key = {fds9392}
}

 

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