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SIAM Journal on Imaging Sciences








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.


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

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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.