Sparsity-based image deblurring with locally adaptive and nonlocally robust regularization

Important structures in photographic images such as edges and textures are jointly characterized by local variation and nonlocal invariance (similarity). Both of them provide valuable heuristics to the regularization of image restoration process. In this paper, we propose to explore two sets of complementary ideas: 1) locally learn PCA-based dictionaries and estimate the sparsity regularization parameters for each coefficient; and 2) nonlocally enforce the invariance constraint by introducing a patch-similarity based term into the cost functional. The minimization of this new cost functional leads to an iterative thresholding-based image deblurring algorithm and its efficient implementation is discussed. Our experimental results have shown that the proposed scheme significantly outperforms several leading deblurring techniques in the literature on both objective and visual quality assessments.