Dynamic Matrix Recovery from Partially Observed and Erroneous Measurements

Abstract

This paper studies the low-rank matrix recovery problem from partially lost and partially corrupted measurements. It shows both analytically and numerically that the recovery performance can be greatly enhanced if one further exploits the temporal correlations among a sequence of low-rank matrices. The matrix recovery problem is formulated as a non-convex optimization problem, and the recovery error is quantified analytically. A fast iterative algorithm is proposed to solve the non-convex problem, and every sequence generated by the algorithm converges to a critical point of the optimization problem. The method is numerically evaluated on the synthetic datasets.