Nonlocal Matrix Rank Minimization Method for Multiplicative Noise Removal

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.