I'm going to step above my (science) pay grade with an idea.  Perhaps it is already being worked on and I just have not heard of it - quite likely.  And perhaps it can't be done; although it seems to me that it could be done.

A couple of years back Hubble captured some images from not long after the big bang.  It was able to capture this via the assistance of a gravitational lens, which magnifies light as it bends around a massive object(s), in the case of these images a cluster of galaxies.  Essentially this magnification gives a boost to an already powerful telescope.  Within these images are arcs that are distorted views of galaxies 12 billion light years away, less than 2 billion years after the big bang.  Amazing.

Here is where I step out of my pay grade...

If we know that gravitational lenses exist, can't we simply (OK maybe simply is the wrong word) develop a device to bring them into focus?  Take a look at the images Hubble captured.  It is nice that they are so distant, but they are also quite distorted.  Could a program be written to look for shapes that have similar shapes (such that they are assumed to be the same objects) but with curved distortions consistent with what you might find due to this gravitational lens effect?  Once these are identified, could not a program be written to reverse or average out the distortion effects so as to provide a clearer, most likely, image of deep space? 

Couldn't we even do this with digital versions of photos already taken, such as the ones referred to herein?  Might not we even find others that we have yet to recognize?