1. An image processing apparatus comprising: processing circuitry including: an extraction circuitry portion that performs motion compensation using, as reference frames, frames formed of decoded images and using motion vectors in images that have been encoded, and that extracts a plurality of motion compensation images having a lower resolution than a prediction image from the reference frames corresponding to the prediction image; and a prediction imaging circuitry portion that performs a filtering process to compensate the plurality of motion compensation images extracted by the extraction circuitry portion for high-frequency components by utilizing correlation in a time direction that is included in the plurality of motion compensation images, thereby generating the prediction image that has a higher resolution than the plurality of motion compensation images, wherein the prediction imaging circuitry portion includes: a converter that converts a resolution of a difference image between the plurality of motion compensation images extracted by the extraction circuitry portion and that increases the resolution of the difference image, a first filter that applies a low-pass filter to the difference image whose resolution has been increased by the converter, a second filter that applies a high-pass filter to an image obtained by applying the low-pass filter by the first filter, and an adder that adds the image obtained by applying the low-pass filter by the first filter and another image obtained by applying the high-pass filter by the second filter to one of the plurality of motion compensation images extracted by the extraction circuitry portion, and that generates the prediction image.