Yes, but... At the end, you're still reconstructing pieces of information from something that was almost destroyed. Picture it this way: there are amazing deconvolution algorithms that can "undo" all sortf of noise and lack of focuse -- but the end result, however good to the original "bad" data isn't nearly as good as a well taken image to begin with.

Disclaimer: I work in image processing, so the example may be a bit obvious to me.