Transform coding at low bit rates introduces artifacts associated with the basis functions of the transform. For example, decompressed images based on the DCT (discrete cosine transform)- like JPEG¹⁶ - exhibit blocking artifacts at low bit rates. This paper proposes a post-processing scheme to enhance decompressed images that is potentially applicable in several situations. In particular, the method works remarkable well in "deblocking" of DCT compressed images. The method is non-linear, computationally efficient, and spatially adaptive - and has the distint feature that it removes artifacts while yet retaining sharp features in the images. An important implication of this result is that images coded using the JPEG standard can be efficiently post-processed to give significantly improved visual quality in the images.