Wow, that is so cool, and such a good writeup. I like the analogy to an encrypted file, and the key being the exact convolution. The amount of information lost is the amount of information in the key.

I wonder if there is some algorithmic way to find the key and tell if it's correct - some dictionary attack, or some loss function that knows if it's close. Perhaps such a thing only works on images that are similar to a training set. It wouldn't work on black and white random dots, since there'd be no way for a computer to grade or know statistics for which deconvolution looks right.