The Masked Matrix Separation Problem: A First Analysis

Abstract

Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been applied on its left. We propose a convex optimization problem to recover the low rank and sparse matrices, which generalizes the robust PCA framework. We provide incoherence conditions for the success of the proposed convex optimizaiton problem, adapting to the masked setting. The ``mask'' matrix can be quite general as long as a so-called restricted infinity norm condition is satisfied. Further analysis on the incoherence condition is provided and we conclude with promising numerical experiments.