1. An image coding apparatus, including: a transform unit which transforms an image to spatial frequency domain so as to generate transform coefficients, each of which corresponds to a pixel of the image; a substitution unit which substitutes a predetermined number of low-order bits with zero values in a bit string of the transform coefficients corresponding to part of a region in the image; and a coding unit which encodes a bit string of the transform coefficients for the entire image sequentially from high-order bits, after substitution by said substitution unit.