TY - JOUR
T1 - Multiplicative noise removal
T2 - Nonlocal low-rank model and its proximal alternating reweighted minimization algorithm
AU - Liu, Xiaoxia
AU - Lu, Jian
AU - Shen, Lixin
AU - Xu, Chen
AU - Xu, Yuesheng
N1 - Funding Information:
\ast Received by the editors January 31, 2020; accepted for publication (in revised form) May 18, 2020; published electronically September 15, 2020. https://doi.org/10.1137/20M1313167 Funding: The research of the second author is partially supported by the Natural Science Foundation of China under grants 61972265 and 11871348, by the Natural Science Foundation of Guangdong Province of China under grant 2020B1515310008, and by the Educational Commission of Guangdong Province of China under grant 2019KZDZX1007. The research of the third author is partially supported by the National Science Foundation under grant DMS-1913039. The research of the fourth author is partially supported by the Natural Science Foundation of China under grant 61872429. The research of the fifth author is partially supported by the National Science Foundation under grant DMS-1912958, and by the Natural Science Foundation of China under grant 11771464. \dagger Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong, 518060, P.R. China (xliu@szu.edu.cn). \ddagger Corresponding author. Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong, 518060, P.R. China (jianlu@szu.edu.cn). \S Department of Mathematics, Syracuse University, Syracuse, NY 13244 (lshen03@syr.edu). \P Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong, 518060, P.R. China (chenxuszu@sina.com). \| Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529 (y1xu@odu.edu).
Funding Information:
The research of the second author is partially supported by the Natural Science Foundation of China under grants 61972265 and 11871348, by the Natural Science Foundation of Guangdong Province of China under grant 2020B1515310008, and by the Educational Commission of Guangdong Province of China under grant 2019KZDZX1007. The research of the third author is partially supported by the National Science Foundation under grant DMS-1913039. The research of the fourth author is partially supported by the Natural Science Foundation of China under grant 61872429. The research of the fifth author is partially supported by the National Science Foundation under grant DMS-1912958, and by the Natural Science Foundation of China under grant 11771464.
Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics.
PY - 2020
Y1 - 2020
N2 - The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex nonsmooth optimization problem having a patchwise data fidelity and a generalized nonlocal low-rank regularization term. To solve this optimization problem, we propose the PARM algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. A theoretical analysis of the proposed PARM algorithm is conducted to guarantee its global convergence to a critical point. Numerical experiments demonstrate that the proposed method for multiplicative noise removal significantly outperforms existing methods, such as the benchmark SAR-BM3D method, in terms of the visual quality of the denoised images, and of the peak-signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) values.
AB - The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex nonsmooth optimization problem having a patchwise data fidelity and a generalized nonlocal low-rank regularization term. To solve this optimization problem, we propose the PARM algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. A theoretical analysis of the proposed PARM algorithm is conducted to guarantee its global convergence to a critical point. Numerical experiments demonstrate that the proposed method for multiplicative noise removal significantly outperforms existing methods, such as the benchmark SAR-BM3D method, in terms of the visual quality of the denoised images, and of the peak-signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) values.
KW - Image restoration
KW - Multiplicative noise removal
KW - Nonlocal low-rank regularization
UR - http://www.scopus.com/inward/record.url?scp=85092162806&partnerID=8YFLogxK
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U2 - 10.1137/20M1313167
DO - 10.1137/20M1313167
M3 - Article
AN - SCOPUS:85092162806
SN - 1936-4954
VL - 13
SP - 1595
EP - 1629
JO - SIAM Journal on Imaging Sciences
JF - SIAM Journal on Imaging Sciences
IS - 3
ER -