The Experts below are selected from a list of 72 Experts worldwide ranked by ideXlab platform
Jongho Park - One of the best experts on this subject based on the ideXlab platform.
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Fast Nonoverlapping Block Jacobi Method for the Dual Rudin--Osher--Fatemi Model.
SIAM Journal on Imaging Sciences, 2019Co-Authors: Chang-ock Lee, Jongho ParkAbstract:We consider Nonoverlapping domain decomposition methods for the Rudin--Osher--Fatemi~(ROF) model, which is one of the standard models in mathematical image processing. The image domain is partitioned into rectangular subdomains and local problems in subdomains are solved in parallel. Local problems can adopt existing state-of-the-art solvers for the ROF model. We show that the Nonoverlapping relaxed Block Jacobi method for a dual formulation of the ROF model has the $O(1/n)$ convergence rate of the energy functional, where $n$ is the number of iterations. Moreover, by exploiting the forward-backward splitting structure of the method, we propose an accelerated version whose convergence rate is $O(1/n^2)$. The proposed method converges faster than existing domain decomposition methods both theoretically and practically, while the main computational cost of each iteration remains the same. We also provide the dependence of the convergence rates of the Block Jacobi methods on the image size and the number of subdomains. Numerical results for comparisons with existing methods are presented.
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fast Nonoverlapping Block jacobi method for the dual rudin osher fatemi model
Siam Journal on Imaging Sciences, 2019Co-Authors: Chang-ock Lee, Jongho ParkAbstract:We consider Nonoverlapping domain decomposition methods for the Rudin--Osher--Fatemi (ROF) model, which is one of the standard models in mathematical image processing. The image domain is partition...
Chang-ock Lee - One of the best experts on this subject based on the ideXlab platform.
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Fast Nonoverlapping Block Jacobi Method for the Dual Rudin--Osher--Fatemi Model.
SIAM Journal on Imaging Sciences, 2019Co-Authors: Chang-ock Lee, Jongho ParkAbstract:We consider Nonoverlapping domain decomposition methods for the Rudin--Osher--Fatemi~(ROF) model, which is one of the standard models in mathematical image processing. The image domain is partitioned into rectangular subdomains and local problems in subdomains are solved in parallel. Local problems can adopt existing state-of-the-art solvers for the ROF model. We show that the Nonoverlapping relaxed Block Jacobi method for a dual formulation of the ROF model has the $O(1/n)$ convergence rate of the energy functional, where $n$ is the number of iterations. Moreover, by exploiting the forward-backward splitting structure of the method, we propose an accelerated version whose convergence rate is $O(1/n^2)$. The proposed method converges faster than existing domain decomposition methods both theoretically and practically, while the main computational cost of each iteration remains the same. We also provide the dependence of the convergence rates of the Block Jacobi methods on the image size and the number of subdomains. Numerical results for comparisons with existing methods are presented.
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fast Nonoverlapping Block jacobi method for the dual rudin osher fatemi model
Siam Journal on Imaging Sciences, 2019Co-Authors: Chang-ock Lee, Jongho ParkAbstract:We consider Nonoverlapping domain decomposition methods for the Rudin--Osher--Fatemi (ROF) model, which is one of the standard models in mathematical image processing. The image domain is partition...
Jaakko Astola - One of the best experts on this subject based on the ideXlab platform.
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Block-median pyramidal transform: analysis and denoising applications
IEEE Transactions on Signal Processing, 2001Co-Authors: Vladimir P. Melnik, Ilya Shmulevich, Karen Egiazarian, Jaakko AstolaAbstract:A nonlinear multiscale pyramidal transform based on Nonoverlapping Block decompositions using the median operation and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of oneand two-dimensional (1-D and 2-D) signals. Various denoising techniques are analyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresholds for denoising applications.
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Block-Median Pyramidal Transform: Analysis and
2001Co-Authors: Vladimir P. Melnik, Ilya Shmulevich, Karen Egiazarian, Jaakko AstolaAbstract:A nonlinear multiscale pyramidal transform based on Nonoverlapping Block decompositions using the median opera- tion and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of one- and two-dimen- sional (1-D and 2-D) signals. Various denoising techniques are ana- lyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresh- olds for denoising applications.
Vladimir P. Melnik - One of the best experts on this subject based on the ideXlab platform.
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Block-median pyramidal transform: analysis and denoising applications
IEEE Transactions on Signal Processing, 2001Co-Authors: Vladimir P. Melnik, Ilya Shmulevich, Karen Egiazarian, Jaakko AstolaAbstract:A nonlinear multiscale pyramidal transform based on Nonoverlapping Block decompositions using the median operation and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of oneand two-dimensional (1-D and 2-D) signals. Various denoising techniques are analyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresholds for denoising applications.
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Block-Median Pyramidal Transform: Analysis and
2001Co-Authors: Vladimir P. Melnik, Ilya Shmulevich, Karen Egiazarian, Jaakko AstolaAbstract:A nonlinear multiscale pyramidal transform based on Nonoverlapping Block decompositions using the median opera- tion and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of one- and two-dimen- sional (1-D and 2-D) signals. Various denoising techniques are ana- lyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresh- olds for denoising applications.
Ilya Shmulevich - One of the best experts on this subject based on the ideXlab platform.
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Block-median pyramidal transform: analysis and denoising applications
IEEE Transactions on Signal Processing, 2001Co-Authors: Vladimir P. Melnik, Ilya Shmulevich, Karen Egiazarian, Jaakko AstolaAbstract:A nonlinear multiscale pyramidal transform based on Nonoverlapping Block decompositions using the median operation and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of oneand two-dimensional (1-D and 2-D) signals. Various denoising techniques are analyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresholds for denoising applications.
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Block-Median Pyramidal Transform: Analysis and
2001Co-Authors: Vladimir P. Melnik, Ilya Shmulevich, Karen Egiazarian, Jaakko AstolaAbstract:A nonlinear multiscale pyramidal transform based on Nonoverlapping Block decompositions using the median opera- tion and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of one- and two-dimen- sional (1-D and 2-D) signals. Various denoising techniques are ana- lyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresh- olds for denoising applications.
