Reweighted scheme for low rank matrix recovery from corruptions

Rank-based analysis is a basic approach for many real world applications. Recently, with the progresses of compressive sensing, an interesting problem was proposed to recover a low-rank matrix from corrupting errors. In this paper, we will address this problem from the perspective of the reweighted approach. The core of the proposed method is a reweighted matrix, which is introduced to iteratively penalize the corrupting errors. Compared with the state-of-the-art algorithm, the reweighted scheme could handle many tough problems and its feasible region is much larger. Moreover, if the recovered rank of the matrix is low enough, it can even cope with non-sparse errors.