Foreground-Background Separation via Generalized Nuclear Norm and Structured Sparse Norm Based Low-Rank and Sparse Decomposition

Yongpeng Yang,Zhenzhen Yang,Jianlin Li,Lu Fan

doi:10.1109/access.2020.2992132

Abstract

Low-rank and sparse decomposition (LRSD) has attracted wide attention in video foreground-background separation and many other fields. However, the traditional LRSD methods have many tough problems, such as the problems of the low accuracy of the surrogate functions of rank and sparsity, ignoring the spatial information of the videos and sensitivity to noise, etc. To deal with these problems, this paper proposes the generalized nuclear norm and structured sparse norm (GNNSSN) method based LRSD for video foreground-background separation, which introduces the generalized nuclear norm (GNN) and the structured sparse norm (SSN) to approximate the rank function and the l 0 -norm of the LRSD method. In addition, we extend our proposed model to a robust model against noise for practical applications, and we called the extended method as the robust generalized nuclear norm and structured sparse norm (RGNNSSN) method. At last, we use the alternating direction method of multipliers (ADMM) to solve our proposed two methods. Experimental results and discussions on video foreground-background separation demonstrate that our proposed two methods have better performances than other LRSD based foreground-background separation methods.

Highlights

The technology of video foreground-background separation [1]–[3] which extracts the key information from video data is a core step in video processing
The second section of this paper proposes the generalized nuclear norm and structured sparse norm (GNNSSN) and RGNNSSN models, and uses the alternating direction method of multipliers to solve the above two proposed models
In order to evaluate the efficiency of the proposed GNNSSN and RGNNSSN methods, a large number of simulation experiments are performed for the video foreground-background separation

Summary

INTRODUCTION

The technology of video foreground-background separation [1]–[3] which extracts the key information from video data is a core step in video processing. The traditional method to deal with this problem is the principal component pursuit (PCP) method [20], [21] This method uses the nuclear norm and the l1-norm to approximate the rank function and the l0-norm of the LRSD model, respectively, and it can be shown as follows: min. Wen et al proposed a Low-rank and sparse decomposition (LRSD) based the generalized non-convex regularization (GNR) method and applied it to video foreground-background separation [35]. Liu et al proposed the low-rank and structured sparse decomposition method (LSD) [41] This method uses a structured sparse induction norm (SSIN) to approximate the sparsity function which adds some structured information when handling the background regions or foreground movements with varying scales. In the fourth section, we give the summarized remarks

THE GENERALIZED NUCLEAR NORM AND

CONVERGENCE ANALYSIS FOR THE PROPOSED

CONCLUSION