Background subtraction from compressive measurements (BSCM) is a fundamental and critical task in video surveillance. Existing methods have limitations for incorporating the structural information and exhibit degraded performance in dynamic background, shadow and complex natural scenes. To address this issue, we propose a new Tucker decomposition-based sparse tensor optimization problem, which makes full use of the spatio-temporal features embedded in the video. The ℓ₀-norm in the objective function is used to constrain the sparseness of the spatio-temporal structure of video foreground, which enhances the spatio-temporal continuity and improves the accuracy of foreground detection. The orthogonality constraints on factor matrices in low-rank Tucker decomposition are used to characterize the spatio-temporal correlation of video background, which enhances low-rank characterization and makes better background estimation. Optimality analysis in terms of Karush-Kuhn-Tucker (KKT) conditions is addressed for the proposed sparse tensor optimization problem and a hard-threshing based alternating direction method of multipliers (HT-ADMM) is designed. Comprehensive experiments are conducted on real-world video datasets to demonstrate the effectiveness and superiority of our approach for BSCM.

压缩测量（BSCM）的背景减法是视频监控中的一项基本且至关重要的任务。现有方法在结合结构信息方面具有局限性，并且在动态背景，阴影和复杂自然场景中表现出退化的性能。为了解决这个问题，我们提出了一个新的基于Tucker分解的稀疏张量优化问题，该问题充分利用了视频中嵌入的时空特征。该ℓ ₀目标函数中的-范数用于约束视频前景的时空结构的稀疏性，增强了时空的连续性，提高了前景检测的准确性。低秩Tucker分解中因子矩阵的正交性约束被用来刻画视频背景的时空相关性，从而增强了低秩刻画的特征并提供了更好的背景估计。针对提出的稀疏张量优化问题，针对Karush-Kuhn-Tucker（KKT）条件进行了最优性分析，并设计了一种基于硬脱粒的乘法器交替方向方法（HT-ADMM）。在现实世界的视频数据集上进行了全面的实验，以证明我们的BSCM方法的有效性和优越性。