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Comment by Udo | Hacker News Reader

A nice Gaussian blur would probably be fine, it's specifically the pixelation technique that's leaking data.

It will be worse than that. Pixellation destroys information, it's not reversible in general. But in this case, what is left is enough for recovery, as source domain (check number) is small. Gaussian blur is theoretically lossless (rounding loss and loss on image edges in practice) - you can take arbitrary image, blur it, reverse and get original+noise

Thanks for making me look deeper into what's going on with common blurring algorithms. My instincts were clearly wrong here, for years I thought reversing blurs wasn't feasible in practice. I was very, very wrong.

Unknown Partial Knowledge is a huge problem in human cognition.

This blew my mind, https://www.youtube.com/watch?v=tyHBnT4PmTE

This is less surprising to me than the gaussian reversal, because this motion-deblurring technique relies on several images of the same object. It's still cool, though :)

Gaussian blur is a 100% reversible! You just sharpen using the same Gaussian settings for a Gaussian sharpen. It's only due to rounding to 8bit per colour that causes it to loose any information.

Isn't that still forwardly deterministic i.e. you can apply the same algorithm to it but at a higher resolution?

Yes it is reversible for practical purposes. There is some data loss on edges, which will manifest as noise on recovered image.

You think the technique mentioned in the article doesn't leak data? It actually leaks more data than a gaussian blur.

Gaussian blur suffers from exactly the same problem, although a different difference function is needed for it.

Gaussian blur is equivalent to an auto key cipher [0] without a key. Each pixel is composed of a couple pixels from the original. With some simple algebra, cross-examining pixels that have values determined by the same origin pixel, you can reverse the operation.

[0] http://en.m.wikipedia.org/wiki/Autokey_cipher

I see that I deserved a schooling on gaussian blur, but

  > You think the technique mentioned in the article doesn't leak data?

yes, I do think it leaks data, which was the correct half of my comment, actually.

Not that it matters now, but I always assumed blurring distorted the data in way way that would make it hard to recover in practice.

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