Double-Weighted Low-Rank Matrix Recovery Based on Rank Estimation

Abstract

Robust principal component analysis (RPCA) has widely application in computer vision and data mining. However, the various RPCA algorithms in practical applications need to know the rank of low-rank matrix in advance, or adjust parameters. To overcome these limitations, an adaptive double-weighted RPCA algorithm is proposed to recover low-rank matrix accurately based on the estimated rank of the low-rank matrix and the reweighting strategy in this paper. More specifically, the Gerschgorin’s disk theorem is introduced to estimate the rank of the low-rank matrix first. Then a double-weighted optimization model through two weighting factors for the low rankness and sparsity is presented. Finally an adaptive double weighted algorithm based on rank estimation is proposed, which can reweight the singular values of low-rank matrix and the sparsity of sparse matrix iteratively. Experimental results show that the proposed double-weighted RPCA algorithm outperforms the state-of-the-art RPCA methods.