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

Zhengqin Xu, Huasong Xing, Shun Fang, Shiqian Wu, Shoulie Xie; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2021, pp. 172-180

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 manually 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.