Year: 2023
Author: Jian Lu, Yuting Ye, Yiqiu Dong, Xiaoxia Liu, Yuru Zou
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1171–1191
Abstract
In recent years, the nuclear norm minimization (NNM) as a convex relaxation of the rank minimization has attracted great research interest. By assigning different weights to singular values, the weighted nuclear norm minimization (WNNM) has been utilized in many applications. However, most of the work on WNNM is combined with the $l^2$-data-fidelity term, which is under additive Gaussian noise assumption. In this paper, we introduce the L1-WNNM model, which incorporates the $l^1$-data-fidelity term and the regularization from WNNM. We apply the alternating direction method of multipliers (ADMM) to solve the non-convex minimization problem in this model. We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise. Numerical results show that our method can effectively remove impulse noise.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2201-m2021-0183
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1171–1191
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Image denoising Weighted nuclear norm minimization $l^1$-data-fidelity term Low rank analysis Impulse noise.