Adaptive Weighted Robust Principal Component Analysis1

Abstract

Robust principal component analysis (RPCA) via the nuclear norm minimization (NNM) is a powerful tool for image processing problems. However, most of NNM methods only consider the number of non-zero singular values of the observation matrix, and ignore the different proportions of data information in different singular values, which are related to the exact rank of clean data and should be treated differently. In this paper, we propose an adaptive weighted RPCA to simultaneously preserve low-rank structure and restore the corrupted parts. In our method, the sum of weighted singular values is included in the objective function of minimization. We first estimate the rank of the clean data contained in the observation data by Gerschgorin disks method. Then the weights are adaptively updated by considering some singular values based on the estimated rank, thus both the number and size of the singular values are considered to recover the low-rank matrix with correct information. Experimental results show that the proposed adaptive weighted RPCA algorithm can achieve better performance under various conditions compared to the existing algorithms.