@demofox @nickappleton which part? Adding noise to an image is like convolvint its histogram with noise PDF.
Therefore, if you deconvolve, you get an approximation of denoising. :)
...and obviously, I wasn't the first one to observe it, my excitement went down when I saw existing papers about it ;)
http://liu.diva-portal.org/smash/get/diva2:360818/FULLTEXT01.pdf