Can't some grad student run an inverse fourier transform
on the digitized views we have, and 'un-defocus' them
a bit?


I doubt that would work. signal to noise issues for one thing.
Also, with video any signal that became "blacker than black" is
effectively clipped off as is thus lost. In crude mathematical terms,
you could multiply something by zero, then you have zero, but after that
you can't ever get back to what you first had.
Similar problem for anything that got saturated (whiter than white).