1. An image compression apparatus, comprising: a processor configured to: generate a reduced image with a reduced resolution by sampling an input image, divide the reduced image into a plurality of blocks, calculate pixel value errors between the plurality of blocks, select, as a representative block, one block, which is one of the plurality of blocks and has the smallest pixel value error, determine filter information including at least one interpolation coefficient with respect to the representative block based on the input image and the reduced image, and generate a bitstream by coding the reduced image and the determined filter information; and memory to store the input image.