A non-monotone alternating directional method for matrix recovery problem

Abstract

The low-rank matrix recovery problem, where the concerned matrix is separable into a low-rank part and a sparse part, has been frequently exploited in the fields of image processing and signal data analysis. In this paper, we propose an alternating directional method equipped with the non-monotone search strategy for solving the low-rank matrix recovery problem, where we apply a single step of the steepest gradient descent method to update variables associated with the low-rank part in parallel and the non-monotone search strategy to update the sparse structure matrix.Theoretically, we prove the global convergence of the proposed algorithm under some mild conditions. The efficiency and effectiveness of the proposed algorithm and superiority of the non-monotone search strategy for improving the performance of algorithms are demonstrated by solving some instances of random matrix recovery problems and background/foreground extraction problems.