Robust Matrix Completion By Exploiting Dynamic Low-Dimensional Structures

Abstract This paper studies the robust matrix completion problem for time-varying models. Leveraging the low-rank property and the temporal information of the data, we develop novel methods to recover the original data from partially observed and corrupted measurements. We show that the reconstruction performance can be improved if one further leverages the information of the sparse corruptions in addition to the temporal correlations among a sequence of matrices. The dynamic robust matrix completion problem is formulated as a nonconvex optimization problem, and the recovery error is quantified analytically and proved to decay in the same order as that of the state-of-the-art method when there is no corruption. A fast iterative algorithm with convergence guarantee to the stationary point is proposed to solve the nonconvex problem. Experiments on synthetic data and real video dataset demonstrate the effectiveness of our method.