Document Type

Article

Publication Date

2020

DOI

10.1137/20m1313167

Publication Title

SIAM Journal on Imaging Sciences

Volume

13

Issue

3

Pages

1595-1629

Abstract

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 non-smooth 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.

Comments

"The Author may post the final published version of the Work on the Author's personal web site and on the web server of the Author's institution, provided that proper notice of the Publisher's copyright is included and that no separate or additional fees are collected for access to or distribution of the work."

First Published in SIAM Journal on Imaging Sciences in Volume 13, Issue 3, published by the Society for Industrial and Applied Mathematics (SIAM).

Copyright © by SIAM.

Unauthorized reproduction of this article is prohibited.

Original Publication Citation

Liu, X. X., Lu, J., Shen, L. X., Xu, C., & Xu, Y. S. (2020). Multiplicative noise removal: Nonlocal low-rank model and its proximal alternating reweighted minimization algorithm. SIAM Journal on Imaging Sciences, 13(3), 1595-1629. https://doi.org/10.1137/20m1313167

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