A sparse tensor optimization approach for background subtraction from compressive measurements

Abstract

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.