An image processing device for processing an original image divided into a plurality of blocks that are made up of a plurality of picture elements from encoded image-data which is obtained by encoding a spatial-frequency component of the block as a plurality of spatial-frequency coefficients, and producing reduced encoded image-data which is encoded data on a reduced image that is obtained by reducing the original image to a given reduction rate. If the block in the encoded image-data of the original image is in an area where the value of the function is small due to gentle change in brightness or color of the image, for example, only the direct-current component coefficient of is used for the block. On the other hand, if the block is in a area where the value of the function is large because the area is a boundary area, for example, such as an outline in the image, limited number of lower spatial frequency-coefficients are used for the block. The number is based on the reduction rate of the image.