As fare as a rigorous demonstration goes, that's what resolution targets are for :)
Anyone have any suggestions for doing the same thing for video?
For video, I suspect there's things like FLIF, but with interframe knowledge, allowing even more compression.
None of these should beat good lossy codecs, but they vastly outperform completely uncompressed data for the stuff people normally capture.
If you somehow capture true random noise, then these wont' work. But most recordings of interest are much more structured, hence compressible.
For the curious: the way these non-exact pattern compressors work is by subtracting out the predicted pattern and then storing the remaining signal, which will be smaller numbers and therefore take less bits to store.
Also image compressors like FLIF vastly outperform general compressors on images.
Disclosure: I'm the author of PackRAW, a tool that does exactly that (https://encode.su/threads/2762-PackRAW)
The open source plugin for the image analysis algorithm with is here: https://github.com/Ades91/ImDecorr
But that's not what they're doing - they're doing something about "image partial phase autocorrelation", which are all words I know but not together. I wonder why the naive method isn't adequate.
It's a good approach to entering a new field, and sometimes (rarely) it actually gets results. But the normal situation is that those in the know have thought of, tried and probably reject all the approaches that a newcomer would come up with in the first 10 minutes.
On the contrary, the fact that they did not use it is good evidence that it is inadequate, given they spent a long time on the problem and I'm sure simpler solutions occurred to them. So I'm agreeing with you here. I'm just expressing interest it knowing why it isn't adequate.
Though for what it's worth I do work a lot with image processing (of trapped atoms though, not biological samples), so my first thoughts are also coming from someone who's spent a decent chunk of time considering these things. My group is actually working at the moment on a method of measuring arbitrary aberrations of an imaging system in order to be able to invert them and obtain better images. This is a more general problem, and the finite resolution of any imaging system comes through clearly, we could definitely determine the resolution via our method (though not from a single-image).