A matrix rank minimization-based regularization method for image restoration

Abstract

Image restoration is a fundamental problem of image processing. In recent years, low-rank minimization (LRM) methods have been extensively applied to this problem to improve the image restoration effects. Due to the theoretical difficulties, the matrix's rank is often replaced by its convex surrogates such as the nuclear norm and the solution can be obtained by solving the Euler-Lagrange equation. In this paper, we propose a model for image restoration by utilizing the matrix rank directly. We design a proximal alternating rank minimization algorithm for solving the model. In each subproblem of the proposed algorithm, the closed-form solution can be easily obtained. The global convergence of the algorithm is also demonstrated by applying the Kudyka-Łojasiewicz property. Numerical experiments show that the proposed method can recover images better than some current state-of-the-art methods in terms of both the recovered measure quantities and visual qualities.