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.

中文翻译：

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基于广义核范数和拉普拉斯尺度混合的视频前景-背景分离的低秩稀疏分解

摘要 低秩稀疏分解（LRSD）由于难以逼近低秩稀疏部分，在视频前景-背景分离等许多领域提出了很大的挑战。在实践中，秩和稀疏度可能无法很好地近似，因为这些传统方法在许多情况下都存在次优问题。在本文中，我们分别采用广义核范数 (GNN) 和拉普拉斯尺度混合 (LSM) 建模来逼近低秩矩阵和稀疏矩阵，并提出了一种称为 GNNLSM 的广义公式，用于非凸低秩和稀疏分解基于 GNN 和 LSM。然后，我们采用乘法器的交替方向法（ADMM）来解决我们提出的问题。