1. An image processing apparatus configured to eliminate mosquito noise from a digitally compressed image having a plurality of color components, the apparatus comprising: a dispersion calculation portion of a control unit configured to calculate, on a color component-by-color component basis, for each pixel contained in the digitally compressed image, a dispersion of pixel values of a plurality of pixels contained in a first region in which that pixel serves as a representative pixel; an ε deriving portion of the control unit configured to derive, for each pixel contained in the digitally compressed image, a greatest value of the plurality of dispersions that respectively correspond to the plurality of color components of that pixel, or a corrected value of the greatest value, as an ε value of an ε filter for that pixel; and a filtering portion of the control unit configured to apply the ε filter to the digitally compressed image.