  Small compression noises, despite being transparent to human eyes, can
adversely affect the results of many image restoration processes, if left
unaccounted for. Especially, compression noises are highly detrimental to
inverse operators of high-boosting (sharpening) nature, such as deblurring and
superresolution against a convolution kernel. By incorporating the non-linear
DCT quantization mechanism into the formulation for image restoration, we
propose a new sparsity-based convex programming approach for joint compression
noise removal and image restoration. Experimental results demonstrate
significant performance gains of the new approach over existing image
restoration methods.
