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Volume 41, Issue 6
Impulse Noise Removal by L1 Weighted Nuclear Norm Minimization

Jian Lu, Yuting Ye, Yiqiu Dong, Xiaoxia Liu & Yuru Zou

DOI: 10.4208/jcm.2201-m2021-0183

J. Comp. Math., 41 (2023), pp. 1171-1191.

Published online: 2023-11

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  • 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.

  • Keywords

Image denoising, Weighted nuclear norm minimization, $l^1$-data-fidelity term, Low rank analysis, Impulse noise.

  • AMS Subject Headings

68U10, 94A08, 90C26, 15A03, 46N10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-41-1171, author = {Lu , JianYe , YutingDong , YiqiuLiu , Xiaoxia and Zou , Yuru}, title = {Impulse Noise Removal by L1 Weighted Nuclear Norm Minimization}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2201-m2021-0183}, url = {http://global-sci.org/intro/article_detail/jcm/22108.html} }
TY - JOUR T1 - Impulse Noise Removal by L1 Weighted Nuclear Norm Minimization AU - Lu , Jian AU - Ye , Yuting AU - Dong , Yiqiu AU - Liu , Xiaoxia AU - Zou , Yuru JO - Journal of Computational Mathematics VL - 6 SP - 1171 EP - 1191 PY - 2023 DA - 2023/11 SN - 41 DO - http://doi.org/10.4208/jcm.2201-m2021-0183 UR - https://global-sci.org/intro/article_detail/jcm/22108.html KW - Image denoising, Weighted nuclear norm minimization, $l^1$-data-fidelity term, Low rank analysis, Impulse noise. AB -

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.

Lu , JianYe , YutingDong , YiqiuLiu , Xiaoxia and Zou , Yuru. (2023). Impulse Noise Removal by L1 Weighted Nuclear Norm Minimization. Journal of Computational Mathematics. 41 (6). 1171-1191. doi:10.4208/jcm.2201-m2021-0183
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