Sparsity-based soft decoding of compressed images in transform domain

We propose a sparsity-based soft decoding approach to restore compressed images directly in the transform domain of compression (DCT domain specifically examined in this paper). Restoring transform coefficients rather than pixel values prevents the propagation of quantization errors in the image domain. As natural images are statistically non-stationary with spatially varying sparse representations, we develop an adaptive block-wise sparsity-based restoration method that learns and exploits local statistics. Specially, for each DCT block, we collect sample blocks via non-local patch grouping to learn a compact dictionary based on principal component analysis. The resulting block-specific dictionary is used to estimate the corresponding DCT coefficients by a technique of collaborative sparse coding, in which the similarity between sample DCT patches used in dictionary construction is further considered. Experimental results are encouraging and demonstrate that the proposed soft decoding approach performs competitively on restoring compressed images against existing methods.