A reweighted nuclear norm minimization algorithm for low rank matrix recovery

In this paper, we propose a reweighted nuclear norm minimization algorithm based on the weighted fixed point method (RNNM-WFP algorithm) to recover a low rank matrix, which iteratively solves an unconstrained L2-Mp minimization problem introduced as a nonconvex smooth approximation of the low rank matrix minimization problem. We prove that any accumulation point of the sequence generated by the RNNM-WFP algorithm is a stationary point of the L2-Mp minimization problem. Numerical experiments on randomly generated matrix completion problems indicate that the proposed algorithm has better recoverability compared to existing iteratively reweighted algorithms.