1. A method for processing an input image to reduce compression-related artifacts, said method comprising: generating a plurality of block transforms of the input image having respective plurality of block-grid locations, wherein each of the block-grid locations is shifted with respect to the block-grid locations in each of the other block transformed images; generating a plurality of respective intermediate transform domain filtered images having modified transform coefficients; assigning per-pixel relative weights to each of the intermediate transform domain filtered images, wherein each of the intermediate transform domain filtered images has different contexts, and wherein the per-pixel relative weights are adaptive to the local context in each of the intermediate transform domain filtered images; computing a weighted average of inverse-transforms of the intermediate transform domain filtered images from the per-pixel relative weights to produce a artifact-reduced image; and outputting the artifact-reduced image.