The old adage stands: "Garbage in, garbage out". You cannot improve lens
performance after acquiring the image. At best you can do what DxO software
does, which is to compensate for vignetting, lens distortions and
aberrations at each focal length of a given lens and at each aperture. I
have it and it works quite well for what it does, but it makes no sense to
try to incorporate it into the camera--much smater to make it a computer app
as DxO has done, where it is easily updatable when new lenses come out or
are added to the database.

Toby

Sounded reasonable to me, back in 2006.

http://groups.google.com/group/rec.photo.digital/msg/b24d36c425621dd3

  BugBear

Look up "deconvolution", "Richardson Lucy"...  You can do some clever
stuff, and with things like chromatic aberration and barrel/pincushion
distortion a lot can be done 'reasonably effectively'.., but when it
comes to 'deeper' optical issues, you run into a problem.  The
algorithms can't tell what may be real data against what is lens-
induced data, and as soon as those two things *overlap* (as they do in
most images), you run into trouble - eg the 'echoes' you will see in
most deconvoluted images.

So these systems are great for some things, and particularly useful in
specialist areas like astronomy (stars being effectively point sources
with little overlap).  Quite useful for CA, very useful for
perspective distortion, somewhat useful for reducing blur to
distinguish/resolve details that weren't clear in the original, but at
the cost of artefacts..

So can you achieve the equivalent of the finest Leica from a Helios
and a bit of software?

Nope.

To some degree, but software cannot remove all problems shooting
general subjects.

The fancy stuff NASA and astronomers use makes a lot of assumptions
about what the objects in images are. IF you know exactly the
properties of an object are, you can optimize software to correct very
well for lens imperfections.  But, the result will only work in
photographing that particular class of objects.

When you only have a hammer, everything looks like a nail.  Nowhere
more true than in image processing :-(

As an example, a fuzzy outline on an object can look just like
defocus.  If you artificially sharpen it, then taking an image of a
fuzzy object makes it look like it has a sharp edge!

I think what you are proposing is called "image processing" and digital
cameras already do that.

First of all, the pattern of blur caused by the lens must be reversible.  
That's not always the case.  Second, any processing of this kind
destroys the precious S/N ratio.  A lower S/N ratio means that the noise
filter is going to do a lot more damage to the photo.

Refocusing using a coded patterned aperture mask:
http://www.merl.com/people/raskar/Mask/

Refocusing using a microlens array:
http://graphics.stanford.edu/papers/lfcamera/lfcamera-150dpi.pdf

Add Helicon Focus and multi-shot capture to the body.

And a big processor and battery.