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Comment by brnt | Hacker News Reader

A Guassian blur is not reversable, information is lost. No research shows otherwise, because it's a mathematical property of the Gaussian transform.

Some methods can be used to find one of many solutions to the blur, where certain high frequency information is preferred over others because we know the end results looks like a human face, and not just any solution. But that only means you can get out many possible faces; if your reconstruction tool only gives you want it was simply over-trained.

[edit] You just updated your post. If you have tagged, unblurred photos of the face in your blurred photo, you can (as expected) constrain the end solutions further. WHat's not clear to me from the paper is whether or not the blurred face was tagged as well. Scenario S3 seems most likely the type of scenario encountered in surveillance programs, where the results are nowhere near 91% accurate.

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> A Gaussian blur is not reversable

This might be narrowly true (it’s hard to recover precisely the original image), but is not really an accurate summary in this context, if the only goal of reversal here is to recognize the face. Deconvolution will quite effectively undo gaussian blur. https://en.wikipedia.org/wiki/Deconvolution https://en.wikipedia.org/wiki/Richardson–Lucy_deconvolution https://en.wikipedia.org/wiki/Blind_deconvolution

In Photoshop, the deconvolution tool is called “Smart Sharpen”, and has a preset for a gaussian PSF.

Ironically I think a Gaussian blur is one of the few transforms that should be totally reversible. Since the Fourier transform of a Gaussian kernel is also Gaussian, it is nonzero everywhere, meaning you can in theory just divide the Fourier transform of the image by the Fourier transform of the kernel to get the original back :)

The quantization to the image colorspace and depth is probably the limiting factor, moreso if dithering is used.

As the resolution increases, the ability to reconstruct a lower resolution image goes up as well, which will be more than enough for most identification purposes.

Security as an accidental quality of a system is not security.

Fair point. Elsewhere in thread it looks like they are using a fixed resolution. I guess at that point it comes down to whether they've left enough mid-frequency content for an algorithm to identify the slightly darker/lighter patches of facial features, and whether that spacing can actually identify a person.

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.

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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