Nonconvex Structural Sparsity Residual Constraint for Image Restoration

This article proposes a novel nonconvex structural sparsity residual constraint (NSSRC) model for image restoration, which integrates structural sparse representation (SSR) with nonconvex sparsity residual constraint (NC-SRC). Although SSR itself is powerful for image restoration by combining the local sparsity and nonlocal self-similarity in natural images, in this work, we explicitly incorporate the novel NC-SRC prior into SSR. Our proposed approach provides more effective sparse modeling for natural images by applying a more flexible sparse representation scheme, leading to high-quality restored images. Moreover, an alternating minimizing framework is developed to solve the proposed NSSRC-based image restoration problems. Extensive experimental results on image denoising and image deblocking validate that the proposed NSSRC achieves better results than many popular or state-of-the-art methods over several publicly available datasets.