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Volume 43, Issue 3
Proximal ADMM Approach for Image Restoration with Mixed Poisson-Gaussian Noise

Miao Chen, Yuchao Tang, Jie Zhang & Tieyong Zeng

DOI: 10.4208/jcm.2212-m2022-0122

J. Comp. Math., 43 (2025), pp. 540-568.

Published online: 2024-11

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  • Abstract

Image restoration based on total variation has been widely studied owing to its edge-preservation properties. In this study, we consider the total variation infimal convolution (TV-IC) image restoration model for eliminating mixed Poisson-Gaussian noise. Based on the alternating direction method of multipliers (ADMM), we propose a complete splitting proximal bilinear constraint ADMM algorithm to solve the TV-IC model. We prove the convergence of the proposed algorithm under mild conditions. In contrast with other algorithms used for solving the TV-IC model, the proposed algorithm does not involve any inner iterations, and each subproblem has a closed-form solution. Finally, numerical experimental results demonstrate the efficiency and effectiveness of the proposed algorithm.

  • Keywords

Image restoration, Mixed Poisson-Gaussian noise, Alternating direction method of multipliers, Total variation.

  • AMS Subject Headings

65K10, 68U10, 94A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-540, author = {Chen , MiaoTang , YuchaoZhang , Jie and Zeng , Tieyong}, title = {Proximal ADMM Approach for Image Restoration with Mixed Poisson-Gaussian Noise}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {3}, pages = {540--568}, abstract = {

Image restoration based on total variation has been widely studied owing to its edge-preservation properties. In this study, we consider the total variation infimal convolution (TV-IC) image restoration model for eliminating mixed Poisson-Gaussian noise. Based on the alternating direction method of multipliers (ADMM), we propose a complete splitting proximal bilinear constraint ADMM algorithm to solve the TV-IC model. We prove the convergence of the proposed algorithm under mild conditions. In contrast with other algorithms used for solving the TV-IC model, the proposed algorithm does not involve any inner iterations, and each subproblem has a closed-form solution. Finally, numerical experimental results demonstrate the efficiency and effectiveness of the proposed algorithm.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2212-m2022-0122}, url = {http://global-sci.org/intro/article_detail/jcm/23549.html} }
TY - JOUR T1 - Proximal ADMM Approach for Image Restoration with Mixed Poisson-Gaussian Noise AU - Chen , Miao AU - Tang , Yuchao AU - Zhang , Jie AU - Zeng , Tieyong JO - Journal of Computational Mathematics VL - 3 SP - 540 EP - 568 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2212-m2022-0122 UR - https://global-sci.org/intro/article_detail/jcm/23549.html KW - Image restoration, Mixed Poisson-Gaussian noise, Alternating direction method of multipliers, Total variation. AB -

Image restoration based on total variation has been widely studied owing to its edge-preservation properties. In this study, we consider the total variation infimal convolution (TV-IC) image restoration model for eliminating mixed Poisson-Gaussian noise. Based on the alternating direction method of multipliers (ADMM), we propose a complete splitting proximal bilinear constraint ADMM algorithm to solve the TV-IC model. We prove the convergence of the proposed algorithm under mild conditions. In contrast with other algorithms used for solving the TV-IC model, the proposed algorithm does not involve any inner iterations, and each subproblem has a closed-form solution. Finally, numerical experimental results demonstrate the efficiency and effectiveness of the proposed algorithm.

Chen , MiaoTang , YuchaoZhang , Jie and Zeng , Tieyong. (2024). Proximal ADMM Approach for Image Restoration with Mixed Poisson-Gaussian Noise. Journal of Computational Mathematics. 43 (3). 540-568. doi:10.4208/jcm.2212-m2022-0122
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