Image data is separated into two components having elements arranged in a checkered pattern. A dummy setting component is obtained of the signal value occurring at the hole position of the first component, which is dummy-set corresponding to the direction of signal change of the first component. The dummy setting component is subtracted from the second component to obtain a difference component, which is the high-frequency component. By performing weighted addition on the signal value occurring at the hole position of component 1 and the signal value of the difference component, an addition dummy setting is obtained, and is then added to component 2 to obtain the low-frequency component. By repeatedly subjecting the low frequency-component to this processing, the image data can be transformed into the high-frequency components and the low-frequency components of a plurality of frequency bands.