Tvrpca+: Low-Rank and Sparse Decomposition Based on Spectral Norm and Structural Sparsity-Inducing Norm

Traditional low-rank sparse decomposition algorithms have trouble obtaining a clear and complete foreground representation in foreground–background separation due to the complex video environment and the noise. For this issue, We propose a more robust and higher-performance low-rank and sparse decomposition algorithm named TVRPCA＋ based on spectral norm, structured sparse norm and total variation (TV) regularization. The structured sparse norm and TV regularization are exploited to suppress noise and obtain much cleaner foregrounds. Spectral norm is used in our algorithm for the low-rank component to address the issue of over-punishment and restore more foreground information. Moreover, an efficient algorithm based on the inexact augmented Lagrange multiplier method is designed to solve the proposed optimization problem. Experimental results show that TVRPCA＋ obtained five top F-measures and three of the second-highest F-measures in eight noise-free test video sequences with complex backgrounds, while the highest average F-measure was also achieved in all ten experimental groups with noise. • The SSN and Spectral norm were first introduced into the TVRPCA framework. • TVRPCA＋ has good performance in suppressing the dynamic background. • The TVRPCA＋ method restores more complete foregrounds. • TVRPCA＋ has good robustness to noise.