Single-Image Super-Resolution via Adaptive Joint Kernel Regression

This paper proposes an adaptive joint kernel regression framework for single-image super-resolution (SR). The basic idea is to regularize the ill-posed reconstruction problem using a regression-based prior that exploits both local structural regularity and nonlocal self-similarity of natural images. To this end, we first generalize the nonlocal means method in the local kernel regression framework, and then extend such generalized regressors to the nonlocal range. Combining them into one single regularization term leads to a joint kernel regression scheme that simultaneously exploits both image statistics in a natural manner. We further propose a measure called regional redundancy to determine the confidence of these regression groups and thus control their relative effects of regularization adaptively. Adaptive dictionary learning and dictionary-based sparsity prior are also introduced to interact with the regression prior for robustness. Quantitative and qualitative results on SR show that our method outperforms other state-of-the-art methods, and can also be applied to other inverse problems such as image deblurring.