1. A filtering device which filters an original image, comprising: a reducing processor that reduces the number of pixels forming said original image so as to generate a low-resolution image; a filtering processor that filters pixel data of pixels forming said low-resolution image so as to transform said low-resolution image into a filtered image; and an image restoring processor that restores the number of pixels forming said filtered image to the number of pixels forming said original image so as to generate a restored image.