Robust principal component analysis via weighted nuclear norm with modified second-order total variation regularization

The traditional robust principal component analysis (RPCA) model aims to decompose the original matrix into low-rank and sparse components and uses the nuclear norm to describe the low-rank prior information of the natural image. In addition to low-rankness, it has been found in many recent studies that local smoothness is also crucial prior in low-level vision. In this paper, we propose a new RPCA model based on weight nuclear norm and modified second-order total variation regularization (WMSTV-RPCA for short), which exploits both the global low-rankness and local smoothness of the matrix. Extensive experimental results show, both qualitatively and quantitatively, that the proposed WMSTV-RPCA can more effectively remove noise, and model dynamic scenes compared with the competing methods.