Here at Astrometry.net headquarters we get a lot of images of the night sky where the exposure is long and the stars have trailed into partial circular arcs. If we could
de-blur these into images of the sky, this would be great: Every one of these trailed images would provide a photometric measurement of every star. Advanced goal: Every one of these trailed images would provide a photometric light curve of every star. That would be sweet! Not sure if this is really research, but it would be cool.
The problem is easy, because every star traverses the same angle in a circle with the same center. Easy! But the problem is hard because the images are generally taken with cameras that have substantial field distortions (distortions in the focal plane away from a pure tangent-plane projection of the sky). Still, it seems totally do-able!
Pedants beware: Of course I know that it is the Earth rotating and not the sky rotating! But yes, I have made that pedantic point on occasion too.