Adjusted Non-Local Regression and Directional Smoothness for Image Restoration

Image restoration (IR) problems are very important in many low-level vision tasks. Due to their ill-posed natures, image priors are widely used to regularize the solution spaces. Recently, patch-based non-local self-similarity has shown great potential in IR problems, leading to many effective non-local priors. Their performance largely depends on whether the non-local self-similarity of the underlying image can be fully exploited. However, most of these priors, including non-local regression (NLR), only utilize the center pixel of each patch to model the non-local feature, which is suboptimal. We propose an effective overlap-based non-local regression (ONLR) to fully exploit the non-local similar patches: first, the concept of overlap-based similar pixels group (OSPG) is introduced; second, for each pixel within an OSPG, the non-local weight is obtained via a novel similarity measurement method; third, based on the consistency assumption, the non-local fitting deviations (NLFDs) by using OSPGs are uniformly constrained. Because of the uniform constraints, the restoration may be poor in regions where OSPGs are not reliable. Consequently, a weighting scheme is proposed to measure the OSPG reliability, leading to a novel adjusted non-local regression (ANLR). In addition, the integral image technique (IIT) is adopted to speed up the similar patches search process. To further boost the ANLR, a local directional smoothness (DS) prior is proposed as a good complement of the non-local feature. Finally, a fast split Bregman iteration algorithm is designed to solve the ANLR-DS minimization problem. Extensive experiments on two typical IR problems, that is, image deblurring and super resolution, demonstrate the superiority of the proposed method compared to many state-of-the-art IR methods.