Inter-block consistent soft decoding of JPEG images with sparsity and graph-signal smoothness priors

Given the prevalence of JPEG compressed images on the Internet, image reconstruction from the compressed format remains an important and practical problem. Instead of simply reconstructing a pixel block from the centers of assigned DCT coefficient quantization bins (hard decoding), we propose to jointly reconstruct a neighborhood group of pixel patches using two image priors while satisfying the quantization bin constraints. First, we assume that a pixel patch can be approximated as a sparse linear combination of atoms from an offline-learned over-complete dictionary. Second, we assume that a patch, when interpreted as a graph-signal, is smooth with respect to an appropriately defined graph that captures the estimated structure of the target image. Finally, neighboring patches in the optimization have sufficient overlaps and are forced to be consistent, so that blocking artifacts typical in JPEG decoded images are avoided. To find the optimal group of patches, we formulate a constrained optimization problem and propose a fast alternating algorithm to find locally optimal solutions. Experimental results show that our proposed algorithm outperforms state-of-the-art soft decoding algorithms by up to 1.47dB in PSNR.