It's impossible not to give you the upvote. It's a perfect post:
mean vs median vs "the value in the galaxy far, far away"
SNR - explained
Why can't I stack the same Image
Actually... Something could be done... Yes it sounds like the mathematical black magic but check the references from Ivica Kopriva. He was working a lot on under-determined blind source separation problems and even succeed to extract multiple components from the single image with and without the extension of dimensionality.
Thank you very much @alexs1320 I will definitely check out Ivica Kopriva's work. However, It does sound like it is more a technique of extracting more out of a single image.
We had tried something for FTIR images, and after extracting the components with the meaning, there is a lot of nice noise to be discarded and some background artefacts. The problem was that it looked a bit ugly (a bit artificial) because there were completely noise-free parts and then the areas with information and some noise. Maybe it will be nicer with your kind of images.