Low-Rank Approximation via the Generalized Reweighted Iterative Nuclear Norm

Abstract

low-rank approximation problem has recently attracted wide concern due to its excellent performance in realworld applications such as image restoration, traffic monitoring, and face recognition. Compared with the classic nuclear norm, the Schatten-p norm is stated to be a closer approximation to restrain the singular values for practical applications in the real world. However, Schatten-p norm minimization is a challenging non-convex, non-smooth, and non-Lipschitz problem. In this paper, inspired by the reweighted $\ell_{1}$ norm for compressive sensing, the generalized iterative reweighted nuclear norm (GIRNN) algorithm is proposed to approximate Schatten-p norm minimization. By involving the proposed algorithms, the problem becomes more tractable and the closed solutions are derived from the iteratively reweighted subproblems. Numerical experiments for the practical matrix completion (MC) problem and robust principal component analysis (RPCA) problem are illustrated to validate the superior performance of both algorithms over some common state-of-the-art methods.