Would it be possible to get a terribly shaped mirror, like a large sheet of something reflective, give it a general shape like a telescope mirror, but not anywhere near as precisely shaped as in a proper mirror, then use software to correct the image collected by the CCD into likely images?
The software could "learn" by being pointed at various objects , sun, moon, planets, stars, houses, etc, to learn it's own mirror errors, which you could correct, with the correction data saved as a filter,,much like facial and object recognition software operates, then use X number of high end graphics cards to correct the image in real time. Seems as though the software correcting for the terribly made mirror would eventually create a filter that would give a good image. Even if the errors required a lot of storage space on drives to create the filter, it should be able to correct the images over time into something recognizable and maybe accurate.
Another thing would be editing software for the image , you could manually or automatically bend the observed objects lines, correction software would straighten or curve lines in initial images, and the correction you apply would be applied to your terrible mirror's error correction filter. Your terrible mirror could be an old silvered Pyrex plate, or a large piece of Mylar balloon material mounted on a shaped frame, or an intentionally formed piece of sheet metal, or such common things with an inaccurate mirror shape that's not ground to a wavelength of light as current mirrors are. Information not received and reflected by the lousy mirror could be filled in by the software after it learns for a while. The cheaper but much larger mirror might fill in some of that lost information~~~