Spherically contoured exponential scale mixture prior based nonlocal image restoration with ADMM framework

According to the nonlocal self-similarity property of natural images, group-based simultaneous sparse coding (GSSC) model assumes that nonlocal similar patches have similar sparse representations in a given dictionary and have been widely used in various image inverse problems. Inspired by the success of the GSSC mode in image restoration problems, this paper proposes a weighted group-based simultaneous sparse coding (WGSSC) model based on the spherically contoured exponential scale mixture (SCESM) prior for image restoration. Compared with traditional GSSC models, which often characterize the similar sparse coefficients by a common set of zero supports and lack spatial adaption and principled fashion, the proposed model considers the dependent relation and adaptivity of similar sparse coefficient, so it is more rational than the GSSC model. The similar sparse coefficients and scale variables can be jointly estimated by the alternating minimization algorithm with the SCESM prior. Based on the estimated sparse coefficients, we can reconstruct the clear patch group and obtain the global denoised image by averaging these patch groups. We refer this denoised method as WGSSC-SCESM based denoiser prior, which can be effectively plugged into general image restoration problems by the alternating direction method of multipliers (ADMM) techniques. Extensive experiments on various types of image restoration problems, e.g., image denoising, inpainting, deblurring and single image super-resolution, demonstrate that the proposed method outperforms many state-of-the-art restored methods in term of the objective and subjective metrics.