Generalized nuclear norm and Laplacian scale mixture based low-rank and sparse decomposition for video foreground-background separation

Abstract

Low-rank and sparse decomposition (LRSD) poses a big challenge problem in video foreground-background separation and many other fields due to its difficulties in approximations of low-rank and sparse parts. The rank and sparsity may not be well approximated in practice since these conventional approaches suffer from the suboptimal issues in many cases. In this paper, we adopt the generalized nuclear norm (GNN) and the Laplacian scale mixture (LSM) modeling to approximate the low-rank and sparse matrices, respectively, and propose a generalized formulation which called GNNLSM for nonconvex low-rank and sparse decomposition based on the GNN and the LSM. And then, we adopt the alternating direction method of multipliers (ADMM) to solve our proposed problem. Simulation results and discussions on video foreground-background separation are given to validate the superiority and the effectiveness of our proposed method.