1. A method of improving the appearance of a decompressed document image while maintaining fidelity with an original document image from which it is derived, wherein for compression, an original document image is divided into blocks of pixels, said blocks of pixels are changed into blocks of transform coefficients by a forward transform coding operation using a frequency space transform operation, said transform coefficients subsequently quantized with a lossy quantization process in which each transform coefficient is quantized according to a quantizing value from a quantization table and the result is used as a quantized transform coefficient, and said blocks of quantized transform coefficients are encoded with a statistical encoding method, the method comprising: a) receiving said statistically encoded, quantized transform coefficient blocks for said original image; b) counting the number of bits representing each block of pixels in said image; c) using said counted number to generate an iteration value; d) removing said statistical encoding to obtain quantized transform coefficients; e) dequantizing the transform coefficients in a block according to a corresponding quantizing value from the quantization table to obtain a block of received transform coefficients; f) recovering the image by applying an inverse transform operation to the received transform coefficients; g) if said iteration number indicates that further appearance improvement is not required, directing the image to an output, and otherwise processing the image with the substeps of: i) filtering the image to improve the appearance thereof; ii) changing the filtered image into blocks of new transform coefficients by the forward transform coding operation; iii) comparing each block of new transform coefficients to the corresponding block of received transform coefficients and the quantization table, to determine whether the filtered recovered image is derivable from the original image; and iv) decrementing the iteration number and returning to f).