A wavelet transform unit performs a wavelet transform on original images and a quantization unit quantizes wavelet transform coefficients. A ROI selector selects a region of interest or regions of interest in the original image, and a ROI mask generator generates ROI masks with which the wavelet transform coefficients (which are also called ROI transform coefficients) corresponding to the regions of interest are specified. By referring to the ROI masks, a lower-bit zero substitution unit substitutes low-order bits of non-ROI transform coefficients with zeros. An entropy coding unit entropy-codes the wavelet transform coefficients sequentially from high-order bit-planes, after the substitution. A coded data generator turns coded data into streams together with parameters and then outputs coded images.