Locally Regularized Collaborative Representation and an Adaptive Low-Rank Constraint for Single Image Superresolution

Abstract

Learning-based superresolution reconstruction is an efficient image processing technique that has become a popular topic in recent years. Since superresolution is an ill-conditioned problem, appropriate image priors or examples are the key factors for recovering high-quality images with rich details. However, in some current advanced superresolution methods, the mappings established using dictionaries of low- and high-resolution examples cannot effectively reflect the relationship between the low- and high-resolution spaces. Therefore, we introduce a local structure prior to the collaborative representation to constrain the projection matrix; this structure can better represent the nonlinear mapping between the low- and the high-resolution feature spaces. Then, based on the redundancy of similar image patches, a shape-adaptive low-rank constraint is utilized to explore the images’ nonlocal self-similarity, and the local and nonlocal priors complement each other to enhance the recovered image quality. Finally, an iterative optimization algorithm is adopted to solve our proposed superresolution model. Numerous experiments were performed to verify the proposed method, and the results demonstrate its superiority to some state-of-the-art methods both quantitatively and qualitatively.