To obtain a highly reliable high image quality expansion image through a simple arrangement by not performing a processing for varying magnification following to an expansion processing, or to generate a image size depending on a use by performing varying magnification.

A user designates an expansion image size for an image already subjected to wavelet conversion (wavelet conversion coefficient) by an image size designating means 1. Subsequently, a hierarchy number (integer) (i) satisfying a directly above layer (i+1) equal to or closest to a designated expansion image size at the inner end, and a directly below layer (i) exceeding, a closest or equal to the designated expansion image size is determined from an image size designated by an image size designating means 1 with reference to a hierarchic wavelet conversion coefficient. More specifically, a hierarchy number (integer) (i) which can be determined uniquely by satisfying the following conditions is calculated. Image size of an original image/2(i+1) ≤ designated image size< image size of the original image/2i.