A wavelet transform is applied to an original image, so as to generate an image of a first hierarchy. Among the thus generated image of the first hierarchy, each of high-frequency sub-band components 1HL, 1LH and 1HH are immediately quantized and coded so as to be temporarily stored in a coded data storage. Another wavelet transform is applied to an LL sub-band component, among the image of the first hierarchy, so as to generate an image of a second hierarchy. Thereafter, an image of a third hierarchy is generated from an LL sub-band component in the image of the second hierarchy. During such a process, quantization and coding processings are performed in parallel with transformation processings. After all processings are completed and the coded data are prepared, coded image data complying with the JPEG2000 standard are generated by first reading out low-frequency components in sequence from the prepared coded data.