I think the place to start would be to combat the noise. It appears that a high ISO was used in order for a fast enough shutter speed to be used so it could be hand held. If instead of hand-holding it, you put it on a tripod, or laid it on a sturdy surface, I bet you could use a much slower tripod (one that would make the photo blurry if it was hand-held), thus allowing the ISO to be much lower, solving the grainy issue.
