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The goal of this paper is to develop a novel numerical method for efficientmultiplicative noise removal. The nonlocal self-similarity of natural imagesimplies that the matrices formed by their nonlocal similar patches arelow-rank. By exploiting this low-rank prior with application to multiplicativenoise removal, we propose a nonlocal low-rank model for this task and develop aproximal alternating reweighted minimization (PARM) algorithm to solve theoptimization problem resulting from the model. Specifically, we utilize ageneralized nonconvex surrogate of the rank function to regularize the patchmatrices and develop a new nonlocal low-rank model, which is a nonconvexnonsmooth optimization problem having a patchwise data fidelity and ageneralized nonlocal low-rank regularization term. To solve this optimizationproblem, we propose the PARM algorithm, which has a proximal alternating schemewith a reweighted approximation of its subproblem. A theoretical analysis ofthe proposed PARM algorithm is conducted to guarantee its global convergence toa critical point. Numerical experiments demonstrate that the proposed methodfor multiplicative noise removal significantly outperforms existing methodssuch as the benchmark SAR-BM3D method in terms of the visual quality of thedenoised images, and the PSNR (the peak-signal-to-noise ratio) and SSIM (thestructural similarity index measure) values.

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