Foreground-Background Separation via Generalized Nuclear Norm and Structured Sparse Norm Based Low-Rank and Sparse Decomposition

Low-rank and sparse decomposition (LRSD) has attracted wide attention in video foreground-background separation and many other fields. However, the traditional LRSD methods have many tough problems, such as the problems of the low accuracy of the surrogate functions of rank and sparsity, ignoring the spatial information of the videos and sensitivity to noise, etc. To deal with these problems, this paper proposes the generalized nuclear norm and structured sparse norm (GNNSSN) method based LRSD for video foreground-background separation, which introduces the generalized nuclear norm (GNN) and the structured sparse norm (SSN) to approximate the rank function and the -norm of the LRSD method. In addition, we extend our proposed model to a robust model against noise for practical applications, and we called the extended method as the robust generalized nuclear norm and structured sparse norm (RGNNSSN) method. At last, we use the alternating direction method of multipliers (ADMM) to solve our proposed two methods. Experimental results and discussions on video foreground-background separation demonstrate that our proposed two methods have better performances than other LRSD based foreground-background separation methods.