Actually it is possible. It has been done to uncover blurred out credit card numbers, for instance. Also, in addition to the methods used in TFA, one can use fractal compression. This matches the 'shapes' in the image to individual fractals, and allows zooming in much further than originally possible without producing pixellation. This is used routinely in the publishing business with low-resolution images, with programs such as this: http://www.ononesoftware.com/detail.php?prodLine_id=2.Unless I am REALLY missing something, it is next to impossible to go from a blurry distorted image to pin-sharp.
So, at least in principle, there's no reason why the software can't do that.