...or Fast Anisotropic Smoothing of Multi-Valued Images by Curvature-Preserving PDE's. Oh well that's clear then. ;)
So what is GREYCstoration? It's a nice mathematical method of cleaning up dirty images. By dirty I mean those with speckles, scratches, JPEG artefacts and various other defects. There's a big gallery of before and after images and some of the results are vey impressive indeed.
It's available as a command line tool but installation sounds a bit fiddly as it relies on various other things being installed. However there's a much easier way to get your hands on it - it's available as a plugin for Gimp.
Oh and it's free. We likes free. :)