Nonconvex Weighted $\ell _p$ Minimization Based Group Sparse Representation Framework for Image Denoising

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, learned simultaneous sparse coding. 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 cannot still obtain the correct sparsity solution under some practical problems including image inverse problems. In this letter, we propose a nonconvex weighted <inline-formula><tex-math notation="LaTeX">$\ell _p$</tex-math></inline-formula> minimization based group sparse representation framework for image denoising. To make the proposed scheme tractable and robust, the generalized soft-thresholding algorithm is adopted to solve the nonconvex <inline-formula><tex-math notation="LaTeX"> $\ell _p$</tex-math></inline-formula> minimization problem. In addition, to improve the accuracy of the nonlocal similar patch selection, an adaptive patch search scheme is proposed. Experimental results demonstrate that the proposed approach not only outperforms many state-of-the-art denoising methods such as BM3D and weighted nuclear norm minimization, but also results in a competitive speed.