Plan of attack....
1) Realize that you have been very lucky with this photo. All of the important parts are relatively intact - eyes, mouths, noses.
2) Don't waste time with the background - just do a new one.
3) Don't waste time with colours, there's nothing worth saving. Convert to greyscale, choose the best channels (Red and Green here) and use the channel mixer;
4) Use healing brush, or similar, for the skin;
5) Use clone for the hair;
6) Colourize (maybe)
Neat image will not help as this is not "noise" with some sort of overall characteristic, it's just random grunge.
Good luck!
Rô