4 research outputs found
Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm
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
Multiplicative Noise Removal: Nonlocal Low-Rank Model and It\u27s Proximal Alternating Reweighted Minimization Algorithm
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