Video Foreground-Background Separation via Weighted Schatten-p Norm and Structured Sparsity Decomposition

In the scenes of dynamic background or measurement noise, the movement background or noise is easily regarded as a part of the foreground. Simultaneously, it is separated by the background modeling algorithm via decomposition of low-rank and sparsity based on the nuclear norm. This algorithm has poor performance in modeling capability of complex backgrounds. To tackle this issue, a video foreground-background separation algorithm via decomposition of weighted Schatten-p norm and structured sparsity is proposed. First, the background matrix is constrained by the weighted Schatten-p norm, which has a better performance for restraining measurement noise than the nuclear norm. Second, the foreground matrix is constrained by the structured sparsity, which uses a structured prior knowledge that the foreground changes continuously in space, and a video background separation model is established. Finally, a decomposition algorithm of the weighted Schatten-p norm and structured sparsity is designed using an augmented Lagrangian method and a generalized soft-thresholding algorithm. The numerical experiment results show that, compared with five other main algorithms, the proposed algorithm can separate objectives more accurately in the scenes of dynamic background.