Stable Analysis of Compressive Principal Component Pursuit

Compressive principal component pursuit (CPCP) recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. Pervious works mainly focus on the analysis of the existence and uniqueness. In this paper, we address its stability. We prove that the solution to the related convex programming of CPCP gives an estimate that is stable to small entry-wise noise. We also provide numerical simulation results to support our result. Numerical results show that the solution to the related convex program is stable to small entry-wise noise under board condition.