Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements

The principal component prsuit with reduced linear measurements (PCP RLM) has gained great attention in applications, such as machine learning, video, and aligningmultiple images.The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee the exact low-rank matrix recovery and sparse matrix recovery as well. In this paper, we prove that the operator of PCP RLM satisfies restricted isometry property (RIP) with high probability. In addition, we derive the bound of parameters depending only on observed quantities based on RIP property, which will guide us how to choose suitable parameters in strongly convex programming.