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You aren't going to get major improvement out of this small, artifacted(from jpg compression) image.  Alot of detail is gone...

 

 With that said. 

 

 My suggestions:

 

 Go into the channels and use the smart blur filter on the worst causes of the artifacts.  Most likely the blue channel for starters.

 

 After that is finished. At 72dpi, and at this size you aren't going to get alot of sharpness out of it without reverting back to some of the jaggie/artifacts.  But, you could focus on the eyes a bit. Making the highlights stand out.  And the hair. While keeping the skin smooth looking(with less banding).

 

 Anyway, here's a quick example. Not much better. But the skin is smoother, most of the nasty artifacts are missing. And it has been color corrected(some). Removed some of the prominent magentas.

 

-Floydski

 I'd look for a better/bigger picture to work from if possible. Or you could blow this up some and work from it.