>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.
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.