Nonlocal image representation or group sparsity has attracted considerableinterest in various low-level vision tasks and has led to severalstate-of-the-art image denoising techniques, such as BM3D, LSSC. In the past,convex optimization with sparsity-promoting convex regularization was usuallyregarded as a standard scheme for estimating sparse signals in noise. However,using convex regularization can not still obtain the correct sparsity solutionunder some practical problems including image inverse problems. In this paperwe propose a non-convex weighted $\ell_p$ minimization based group sparserepresentation (GSR) framework for image denoising. To make the proposed schemetractable and robust, the generalized soft-thresholding (GST) algorithm isadopted to solve the non-convex $\ell_p$ minimization problem. In addition, toimprove the accuracy of the nonlocal similar patches selection, an adaptivepatch search (APS) scheme is proposed. Experimental results have demonstratedthat the proposed approach not only outperforms many state-of-the-art denoisingmethods such as BM3D and WNNM, but also results in a competitive speed.
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