Generating artifacts is a major problem with compressed images coded by the block discrete cosine transform (BDCT). An iterative deblocking method based on projection onto convex sets (POCS) is presented in this paper. The method considers pixel-wise local adaptability. The adjustment of a pixel is determined by local properties of the pixel. A coded image is iteratively projected onto two locally adaptive smoothness constraint sets, a locally adaptive quantization constraint set and an intensity constraint set to obtain an improved image where artifacts are reduced. The proposed method is tested on JPEG encoded images with excellent results.