Robust Image Restoration via Reweighted Low-Rank Matrix Recovery

In this paper, we propose a robust image restoration method via reweighted low-rank matrix recovery. In the literature, Principal Component Pursuit (PCP) solves low-rank matrix recovery problem via a convex program of mixed nuclear norm and ℓ1 norm. Inspired by reweighted ℓ1 minimization for sparsity enhancement, we propose reweighting singular values to enhance low rank of a matrix. An efficient iterative reweighting scheme is proposed for enhancing low rank and sparsity simultaneously and the performance of low-rank matrix recovery is prompted greatly. We demonstrate the utility of the proposed method on robust image restoration, including single image and hyperspectral image restoration. All of these experiments give appealing results on robust image restoration.