An image processing apparatus in which image data is transformed to spatial frequencies to obtain multiple frequency components, the obtained frequency components are processed, the processed frequency components are inversely transformed to image data, and the number of gray levels of the inversely transformed image data is decreased, and the image processing apparatus comprising a frequency component judgment section for comparing the absolute value of each of specific multiple frequency components in the multiple frequency components obtained after transformation to spatial frequencies with a predetermined value in terms of magnitude, a frequency component changing section for changing each of specific frequency components on the basis of the result of the comparison, and a noise addition section for adding a specific value to each of the specific frequency components having been changed and other frequency components.