A Graph Regularized RPCA by Generalized Moreau Enhanced Model

A robust principal component analysis (RPCA) on graphs [Shahid et al., 2016] shows that a quadratic function, say the graph regularizer, designed with two graph Laplacians, can serve as a computationally efficient low-rankness promoting regularizer. In this paper, we present a novel RPCA by combining the graph regularizer with a generalized-Moreau-nonconvex-enhancement of L1 norm. The proposed graph regularized RPCA (GRPCA) model uses a nonconvex penalty while maintaining the overall convexity and can be solved with a proximal splitting type algorithm in [Abe, Yamagishi, and Yamada, 2020]. A numerical experiment in a scenario of foreground and background decomposition of a video demonstrates the efficacy of the proposed GRPCA