  Nonlocal image representation or group sparsity has attracted considerable
interest in various low-level vision tasks and has led to several
state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past,
convex optimization with sparsity-promoting convex regularization was usually
regarded as a standard scheme for estimating sparse signals in noise. However,
using convex regularization can not still obtain the correct sparsity solution
under some practical problems including image inverse problems. In this paper
we propose a non-convex weighted $\ell_p$ minimization based group sparse
representation (GSR) framework for image denoising. To make the proposed scheme
tractable and robust, the generalized soft-thresholding (GST) algorithm is
adopted to solve the non-convex $\ell_p$ minimization problem. In addition, to
improve the accuracy of the nonlocal similar patches selection, an adaptive
patch search (APS) scheme is proposed. Experimental results have demonstrated
that the proposed approach not only outperforms many state-of-the-art denoising
methods such as BM3D and WNNM, but also results in a competitive speed.
