But is deblurring from handshake or lens out of focus or even a Gaussian blur the same as some random gradient blur they seem to be using?

Edit: The images in the Signal article don't look like images of blurred faces. They look like blurry images overlaid onto faces. If you don't blur the face, how can it be unblurred?

Yes, they are using a 25px Gaussian blur, they are not overlaying a different image on top: https://news.ycombinator.com/item?id=23415600

Impressive examples. Thanks for posting them!

So the ridiculous „Enhance!“ one sees in TV show crime dramas could one day actually become true.

You can't make data that isn't there. It's fundamentally going to be a guess. You can enhance your way to a face or a license plate but there is zero guarantee it will be the face or the license plate that the low quality image/video is of. This is why solid blocks of color or emojis are so effective at censoring images, it takes the data and replaces it with pure junk.

If you know it's a gaussian blur with a known radius, you can uniquely reverse it.

You do, however, lose colour depth information (e.g. deep color to true colour, true colour to high colour / 256 colours). Still enough to detect a face.

Yes, that works if the face itself is blurred, not if random noise is used in place of the face.

They're not using random noise in place of the face, they're using a 25px Gaussian blur: https://news.ycombinator.com/item?id=23415600

Nice find. That is unfortunate then. I thought they'd make more effort.