Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm

TL;DR

This paper introduces a novel nonlocal low-rank model and a proximal alternating reweighted minimization algorithm for efficient multiplicative noise removal, leveraging nonlocal self-similarity and low-rank priors to improve image denoising quality.

Contribution

It proposes a new nonlocal low-rank model with a nonconvex surrogate for multiplicative noise removal and develops a convergent optimization algorithm tailored for this model.

Findings

Outperforms existing methods like SAR-BM3D in visual quality.

Achieves higher PSNR and SSIM values.

Demonstrates effective convergence of the proposed algorithm.

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 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 the PSNR (the peak-signal-to-noise ratio) and SSIM (the structural similarity index measure) values.