Nonlocal Matrix Rank Minimization Method for Multiplicative Noise Removal

doi:10.1007/s42967-024-00396-9

摘要/Abstract

摘要： Multiplicative noise removal is a challenging problem in image denoising. In this paper, we develop a nonlocal matrix rank minimization method for the multiplicative noise removal problem. By utilizing the logarithm transformation, we convert the problem into an additive noise removal problem and propose a maximum a posteriori (MAP) estimation-based matrix rank minimization model for this kind of additive noise removal. A proximal alternating algorithm is designed to solve the matrix rank minimization model. The convergence of the algorithm is demonstrated by the famous Kurdyka-Łojasiewicz property. Taking advantage of the proposed matrix rank minimization model and its proximal alternating algorithm, a multiplicative noise removal method is finally developed. Numerical experiments illustrate that the proposed method can remove multiplicative noise in images much better than the existing state-of-the-art methods in terms of both image recovered measure quantities and visual qualities.

关键词: Multiplicative noise, Matrix rank minimization, Proximal alternating method, Kurdyka-Łojasiewicz property

Abstract: Multiplicative noise removal is a challenging problem in image denoising. In this paper, we develop a nonlocal matrix rank minimization method for the multiplicative noise removal problem. By utilizing the logarithm transformation, we convert the problem into an additive noise removal problem and propose a maximum a posteriori (MAP) estimation-based matrix rank minimization model for this kind of additive noise removal. A proximal alternating algorithm is designed to solve the matrix rank minimization model. The convergence of the algorithm is demonstrated by the famous Kurdyka-Łojasiewicz property. Taking advantage of the proposed matrix rank minimization model and its proximal alternating algorithm, a multiplicative noise removal method is finally developed. Numerical experiments illustrate that the proposed method can remove multiplicative noise in images much better than the existing state-of-the-art methods in terms of both image recovered measure quantities and visual qualities.

Key words: Multiplicative noise, Matrix rank minimization, Proximal alternating method, Kurdyka-Łojasiewicz property

Hui-Yin Yan. Nonlocal Matrix Rank Minimization Method for Multiplicative Noise Removal[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1744-1768.

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