In this paper, a novel projection onto convex sets (POCS) method is presented for the suppression of blocking and ringing artifacts in a compressed image that contains homogeneous regions. A new family of convex smoothness constraint sets is introduced, using the uniformity property of image regions. This set of constraints allows different degrees of smoothing in different regions of the image, while preserving the image edges. The regions are segmented using the fuzzy c-means algorithm, which allows ambiguous pixels to be left unclassified. Experimental results on JPEG compressed images demonstrate that the proposed algorithm yields visually superior images compared to several of the recently reported POCS deblocking algorithms for the class of images considered.