Low-rank matrix recovery based on smooth function approximation

Abstract

Recently, smooth rank function was proposed for matrix completion problem. The main idea of this method was based on a continuous and differentiable approximation of the rank function. In this paper, a new approach for solving low-rank matrix recovery problem based on smooth function is proposed. It not only uses a smooth function to approximate the rank function, but also approximates the l 0 -norm with a continuous and differentiable function. In addition, gradient decreasing approach can be used to solve the minimization problem. Finally, experimental results show that this new algorithm provides accurate results in almost all of our testing scenarios with a reasonable running time. Especially, it has higher approximation performance than other methods.