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 - <p style="text-align: justify;">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.</p>