>If they applied a perfect digital gaussian-blur, then that is reversible
Not true. Deconvolution is a statistical estimate. Think about it. When you blur, colors get combined with their neighbors. Statistically this moves toward a middle grey. You're compressing the gamut of colors towards the middle, and thus losing information. Look at an extreme case - 2 pixels of mid-grey. It can be deconvoluted to itself, to a light and dark grey, or to one black and one white. All those deconvolutions are equally valid. There's no 1-to-1 inverse to a convolution. If you do a gaussian blur on a real photo and then a deconvolution algorithm you'll get a different image, with an arbitrary tuning, but probably biased towards max contrast in details and light noise, since that what people expect from such tools and what most real photos have. But, just like A.I. enhanced images, it's using statistics when filling in the missing data.
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.
Not true. Deconvolution is a statistical estimate. Think about it. When you blur, colors get combined with their neighbors. Statistically this moves toward a middle grey. You're compressing the gamut of colors towards the middle, and thus losing information. Look at an extreme case - 2 pixels of mid-grey. It can be deconvoluted to itself, to a light and dark grey, or to one black and one white. All those deconvolutions are equally valid. There's no 1-to-1 inverse to a convolution. If you do a gaussian blur on a real photo and then a deconvolution algorithm you'll get a different image, with an arbitrary tuning, but probably biased towards max contrast in details and light noise, since that what people expect from such tools and what most real photos have. But, just like A.I. enhanced images, it's using statistics when filling in the missing data.