A Variational Approach for Sparse Component Estimation and Low-Rank Matrix Recovery

The problem of estimating low-rank matrices in the presence of sparse outliers has drawn significant attention recently. A typical example is robust principal component analysis (RPCA), where the high-dimensional data lying in a low-dimensional subspace are subject to the perturbation of a few outliers. Recently, theoretical performance guarantees for RPCA have been provided in [8], where it is shown that the RPCA problem can be solved using convex optimization. In addition, RPCA has been applied to solve a wide range of problems [12, 15, 17, 21] and its advantage has been demonstrated [28, 30, 38, 39].