SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1595-1629, January 2020.
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.

中文翻译：

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乘法噪声消除：非局部低秩模型及其近交交替加权最小化算法

SIAM影像科学杂志，第13卷，第3期，第1595-1629页，2020年1月。
本文的目的是开发一种有效去除乘性噪声的新颖数值方法。自然图像的非局部自相似性意味着由其非局部相似斑块形成的矩阵是低秩的。通过将这种低秩优先级应用于乘除噪声，我们提出了一种针对该任务的非局部低秩模型，并开发了一种近端交替重加权最小化（PARM）算法来解决该模型导致的优化问题。具体来说，我们利用秩函数的广义非凸替代规则对补丁矩阵进行正则化，并开发了一个新的非局部低秩模型，该模型是具有凸面数据保真度和广义非局部低秩正则化项的非凸非光滑优化问题。为了解决此优化问题，我们提出了PARM算法，该算法具有一个近端交替方案，其子问题经过重新加权近似。对所提出的PARM算法进行了理论分析，以确保其全局收敛到一个临界点。数值实验表明，所提出的乘除噪方法在去噪图像的视觉质量和峰值信噪比（PSNR）方面明显优于现有方法，例如基准SAR-BM3D方法以及结构相似性指标度量（SSIM）值。