1. An image encoding apparatus, comprising: an image dividing unit to generate a plurality of actual images of respective areas divided from an input image, the respective areas being different from each other; an image filtering unit to predictive-filter each of the plurality of actual images using a predictive filter to generate a predicted image with respect to each of the plurality of actual images; an image operating unit to generate a difference image corresponding to each of the plurality of actual images based on respective comparisons of the predicted images and the actual images corresponding to the predicted images; an image selecting unit to select at least one difference image, of the generated difference images, based on respective data magnitudes of the difference images; and an image encoding unit to encode the selected difference image, a filter coefficient of the predictive filter corresponding to a predicted image used to generate the selected difference image, and an actual image, from among the plurality of actual images, in which a corresponding difference image is not selected by the image selecting unit.