Communications on Applied Mathematics and Computation >

2021 , Vol. 3 >Issue 3: 371 - 390

DOI: https://doi.org/10.1007/s42967-020-00076-4

Weighted Nuclear Norm Minimization-Based Regularization Method for Image Restoration

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  • 1 Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
    2 School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan Province, China

Received date: 2019-07-28

  Revised date: 2020-03-25

  Online published: 2021-09-16

Supported by

This work is supported by the National Natural Science Foundation of China nos. 11971215 and 11571156, MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China.

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Abstract

Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem. Different assumptions or priors on images are applied in the construction of image regularization methods. In recent years, matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved. Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix's weighted nuclear norm minimization (WNNM). The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method. In this paper, we develop a model for image restoration using the sum of block matching matrices' weighted nuclear norm to be the regularization term in the cost function. An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented. Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.

Key words： Image restoration; Regularization method; Weighted nuclear norm; Alternating iterative method

Cite this article

Yu-Mei Huang, Hui-Yin Yan . Weighted Nuclear Norm Minimization-Based Regularization Method for Image Restoration[J]. Communications on Applied Mathematics and Computation, 2021 , 3(3) : 371 -390 . DOI: 10.1007/s42967-020-00076-4

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