Overlapping group prior for image deconvolution using patch-wise gradient statistics

Abstract

In image deconvolution problems, global gradient statistics serve as powerful image priors that separate high-quality images from degraded observations. However, it is unclear whether the important detailed information is sufficiently regularized in these approaches. Owing to the limitations, the restored images exhibit sharply reconstructed edges around structures, but commonly suffer from the loss of significant textures and details. In this study, we introduced patch-wise gradient statistics as an image prior strategy to restore disregarded regions in consideration of regional characteristics. The analytic relation between the prior and the restored local statistics was investigated through the Bayesian interpretation of overlapping group sparsity. The regularization function that incorporates the contextual information was derived in the maximum a posteriori framework. Subsequently, the unknown prior information and latent image were alternately estimated from the observations based on the patch-wise statistical analysis of the non-blind deconvolution process. In the experimental results, the superiority of the proposed algorithm was verified by more original textures in the restored images compared to the conventional approaches.