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Wait: informations is lost if the blur is truly a gaussian process. The simulation of blur by means of a convolution can perfectly well be reversible.

Image blur is not a gaussian process.

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Are you saying that convolution with a gaussian kernel is not real gaussian blur?

I'm legitimately asking. I'm really ignorant about this subject.

In theory it is, in reality there is discretization of the signal and noise

No: it is a simulation, because it is a discretization and the map can be injective (or “almost so”).

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