Adaptive Rank Estimate in Robust Principal Component Analysis

Robust principal component analysis (RPCA) and its variants have gained wide applications in computer vision. However, these methods either involve manual adjustment of some parameters, or require the rank of a low-rank matrix to be known a prior. In this paper, an adaptive rank estimate based RPCA (ARE-RPCA) is proposed, which adaptively assigns weights on different singular values via rank estimation. More specifically, we study the characteristics of the low-rank matrix, and develop an improved Gerschgorin disk theorem to estimate the rank of the low-rank matrix accurately. Furthermore in view of the issue occurred in the Gerschgorin disk theorem that adjustment factor need to be manually pre-defined, an adaptive setting method, which greatly facilitates the practical implementation of the rank estimation, is presented. Then, the weights of singular values in the nuclear norm are updated adaptively based on iteratively estimated rank, and the resultant low-rank matrix is close to the target. Experimental results show that the proposed ARE-RPCA outperforms the state-of-the-art methods in various complex scenarios.