1. A method of losslessly decoding signals representing an image, the method comprising: receiving a lossy compressed data file; receiving a residual compressed data file; separating the lossy compressed data file into DC coefficients and AC coefficients; decoding, separately, the DC coefficients to determine DC values and the AC coefficients to determine AC values; and inverse quantizing the DC values and the AC values to produce lossy, decompressed data; decoding the residual compressed data file to produce a residual decompressed data; combining the lossy decompressed frequency data with the residual decompressed data to produce a lossless data file, wherein the lossless data file is substantially the same as the original image.