Generalized Rank Minimization based Group Sparse Coding for Low-level Image Restoration via Dictionary Learning

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration with group contains low-rank property. In this paper, we introduce a novel GSC framework using generalized rank minimization for image restoration tasks via an effective adaptive dictionary learning scheme. For a more accurate approximation of the rank of group matrix, we proposed a generalized rank minimization model with a generalized and flexible weighted scheme and the generalized nonconvex nonsmooth relaxation function. Then an efficient generalized iteratively reweighted singular-value function thresholding (GIR-SFT) algorithm is proposed to handle the resulting minimization problem of GSC. Our proposed model is connected to image restoration (IR) problems via an alternating direction method of multipliers (ADMM) strategy. Extensive experiments on typical IR problems of image compressive sensing (CS) reconstruction, inpainting, deblurring and impulsive noise removal demonstrate that our proposed GSC framework can enhance the image restoration quality compared with many state-of-the-art methods.