Rank-based analysis is a basic approach for many real world applications. Recently, with the developments of compressive sensing, an interesting problem was proposed to recover a lowrank matrix from sparse noise. In this paper, we will address this problem and propose a low rank matrix recovery algorithm based on sparsity tacking. The core of the proposed Sparsity Tracking Recovery(STR) is a heuristic kernel, which is introduced to penalize the noise distribution. With the heuristic method, the sparse entries in the noise matrix can be accurately tracked and discouraged to be zero. Compared with the state-of-the-art algorithm, STR could handle many tough problems and its feasible region is much larger. Besides, if the recovered rank of the matrix is low enough, it can even cope with non-sparse noise distribution.
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