The answer is No.

After some offline discussions, the inventors of the PFCA seem to have a very good handle on getting a better looking Mona Lisa. This is outstanding as we all look forward to better images from this device. It also looks like some of the readership of Nuit Blanche is growing and somehow changing :-) A commenter said recently:

From what i understand, the blurred image is the result not much of the processing, but from the hardware limitation

I initially responded with: "No" but eventually felt this answer was too terse, let me re-frame it:

Compressive sensing has the potential to improve on the current approach for calibrating this imager. The physical limitations of this device are, in my view, not even reached.

Compressive sensing is not about getting into fashionable papers to get new grants and fame, etc..... It's about making sure that new detectors are the embodiments of our understanding that Nature is governed by power laws and that, finally, terabytes of data will actually mean something..