A support-denoiser-driven framework for single image restoration

Model-based methods have been the powerful strategies for solving a variety of imaging inverse problems. Particularly, the sparsity-enforcing regularization models have been especially widely investigated and adopted over the past decades. Along this research direction, one of the most important topics is the model formulation that is able to incorporate the more suitable image priors. In this paper, we propose a universal and flexible image restoration model that exploits the local sparsity, support and nonlocal denoiser priors simultaneously. While the proposed model is nonconvex as a whole, we show that it can be naturally tackled via a multi-stage convex relaxation procedure based on an extended alternating direction method of multiplier (ADMM) algorithm. Comprehensive numerical experiments demonstrate the effectiveness of our proposed algorithm over many existing state-of-the-art methods, in both objective and perceptual quality.