What is needed for decoding an image compressed by Shapiro's algorithm is the initial threshold, the original image size, the subband decomposition scale and, of course, the encoded bit stream. The decoder then decompresses the arithmetically encoded files into symbol files, creates all the proper size subbands needed since it knows the subband decomposition scale and the original image size, and proceeds to undo the Shapiro compression since it knows the initial threshold and the subband scanning order.