Noise degrades the performance of any image compression algorithm. However,
at very low bit rates, image coders effectively filters noise that may be
present in the image, thus, enabling the coder to operate closer to the noi
se free case. Unfortunately, at these low bit rates the quality of the comp
ressed image is reduced and very distinctive coding artifacts occur. This p
aper proposes a combined restoration of the compressed image from both the
artifacts introduced by the coder along with the additive noise. The propos
ed approach is applied to images corrupted by data-dependent Poisson noise
and to images corrupted by film-grain noise when compressed using a block-t
ransform-coder such as JPEG. This approach has proved to be effective in te
rms of visual quality and peak signal-to-noise ratio (PSNR) when tested on
simulated and real images.