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Recently, low-rank matrix recovery theory has been emerging as a significantprogress for various image processing problems. Meanwhile, the group sparsecoding (GSC) theory has led to great successes in image restoration (IR)problem with each group contains low-rank property. In this paper, we propose anovel low-rank minimization based denoising model for IR tasks under theperspective of GSC, an important connection between our denoising model andrank minimization problem has been put forward. To overcome the bias problemcaused by convex nuclear norm minimization (NNM) for rank approximation, a moregeneralized and flexible rank relaxation function is employed, namely weightednonconvex relaxation. Accordingly, an efficient iteratively-reweightedalgorithm is proposed to handle the resulting minimization problem combing withthe popular L_(1/2) and L_(2/3) thresholding operators. Finally, our proposeddenoising model is applied to IR problems via an alternating direction methodof multipliers (ADMM) strategy. Typical IR experiments on image compressivesensing (CS), inpainting, deblurring and impulsive noise removal demonstratethat our proposed method can achieve significantly higher PSNR/FSIM values thanmany relevant state-of-the-art methods.

From Group Sparse Coding to Rank Minimization: A Novel Denoising Model for Low-level Image Restoration