在具有动态背景或测量噪声的场景中,基于核范数约束的低秩稀疏分解背景建模算法容易将运动的背景或噪声作为前景的一部分与前景同时分离出来,对复杂背景的建模性能表现不佳。针对此问题,提出一种加权Schatten-p范数与结构化稀疏分解的视频前背景分离算法。首先,因加权Schatten-p范数比核范数能够更好地抑制测量噪声,故采用加权Schatten-p范数对背景矩阵进行约束;其次,利用前景在空间上具有连续变化这一结构先验知识,对前景矩阵采用结构化稀疏约束,并在此基础上建立一种视频前背景分离模型;最后,利用增广拉格朗日方法与广义软阈值算法,设计了加权Schatten-p范数与结构稀疏分解算法。数值实验表明:与其他5种主流算法相比,所提算法在具有动态背景的场景中能更准确地分离目标。

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.