Robust Principal Component Analysis via Decomposition into Low-rank and Sparse Matrices: An overview

Authors: T. Bouwmans (Lab MIA, Univ. La Rochelle, France), E. Zahzah (Lab L3i, Univ. La Rochelle, France)

Chapter Description

RPCA via decomposition in low-rank and sparse matrices proposed by Candes et al. in 2009 is currently the most investigated RPCA method. In this chapter, we reviewed this method and all these modifications in terms of decomposition, solvers, incremental algorithms and real time implementations. These different RPCA methods via decomposition in low rank and sparse matrices are fundamental and can be applied to several applications in image and video processing: image analysis, image denoising, motion saliency detection, video coding, key frame extraction, hyperspectral video processing, and background and foreground separation. Here, we choose to focus on the application of background and foreground separation which is a representative application of RPCA, and which witnessed very numerous papers (more than 190) since 2009. Applying RPCA via decomposition in low rank and sparse matrices in video-surveillance, the background sequence is modeled by the low-rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. So, the different advances in the different frameworks of the decomposition in low rank and additive matrices are fundamental and can be applied to background modeling and foreground detection in video surveillance.