1. An image processing apparatus for performing filter processing on a decoded image that is obtained by decoding compressed data obtained by coding a multi-valued image by the block of M×N pixels so as to eliminate noises and generating a reconstructed image, the image processing apparatus comprising: a differential value calculation unit operable to calculate a differential value between a pixel value of a current pixel and each one of pixel values of peripheral pixels in a filter processing area that is predetermined for each pixel that forms the decoded image, a distribution coefficient calculation unit operable to calculate distribution coefficients as to the pixel values of the pixels, a filter coefficient calculation unit operable to calculate the filter coefficients as to the peripheral pixels based on the differential values calculated by the differential value calculation unit and the distribution coefficients calculated by the distribution coefficient calculation unit, and a filter processing unit operable to perform filter processing as to the pixel value of the current pixel in the decoded image using the filter coefficient calculated by the filter coefficient calculation unit and calculate the pixel value of the current pixel in the reconstructed image.