Multiplicative noise removal: Nonlocal low-rank model and its proximal alternating reweighted minimization algorithm

Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1595-1629
Number of pages35
JournalSIAM Journal on Imaging Sciences
Issue number3
StatePublished - 2020


  • Image restoration
  • Multiplicative noise removal
  • Nonlocal low-rank regularization

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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