One salient point not touched on here, is that an awful lot of the time, the things folks are blurring out specifically is text. And since we know an awful lot about what text ought to look like, we have a lot more information to guide the reconstruction...
Captain Disillusion recently covered this subject in a more popular science format as well
Can this be applied to camera shutter/motion blur, at low speeds the slight shake of the camera produces this type of blur. This is usually resolved with IBIS to stabilize the sensor.
The ability to reverse is very dependent on the transformation being well known, in this case it is deterministic and known with certainty. Any algorithm to reverse motion blur will depend on the translation and rotation of the camera in physical space, and the best the algorithm could do will be limited by the uncertainty in estimating those values.
If you apply a fake motion blur like in photoshop or after effects then that could probably be reversed pretty well.
Encode the image as a boundary condition of a laminar flow and you can recover the original image from an observation.
If, however, you observe after turbulence has set in, then some of the information has been lost, it's in the entropy now. How much, that depends on the turbulent flow.
Don't miss out on this video by smarter every day
https://youtu.be/j2_dJY_mIys?si=ArMd0C5UzbA8pmzI
Treat the dynamics and time of evolution as your private key, laminar flow is a form of encryption.
reminds me of the guy who used the photoshop swirl effect to mask his face in csam he produced, who was found out when someone just undid the swirl
My (admittedly superficial) knowledge about blur reversibility is that an attacker may know what kind of stuff is behind the blur.
I mean knowledge like "a human face, but the potential set of humans is known to the attacker" or even worse "a text, but the font is obvious from the unblurred part of the doc".
This was also my understanding.
It's essentially like "cracking" a password when you have its hash and know the hashing algorithm. You don't have to know how to reverse the blur, you just need to know how to do it the normal way, you can then essentially brute force through all possible characters one at a time to see if it looks the same after applying the blur.
Thinking about this, adding randomness to the blurring would likely help.
Or far more simply, just mask the sensitive data with a single color which is impossible to reverse (for rasterized images, this is not a good idea for PDFs which tend to maintain the text "hidden" underneath).
> mask the sensitive data with a single color which is impossible to reverse
You note the pitfall of text remaining behind the redaction in PDFs (and other layered formats), but there are also pitfalls here around alpha channels. There have been several incidents where folks drew not-quite-opaque redaction blocks over their images.
> just mask the sensitive data with a single color which is impossible to reverse (for rasterized images, this is not a good idea for PDFs
Also not a good idea for masking already compressed images of text, like jpg, because some of the information might bleed out in uncovered areas.
The parade is easy: just add a small amount of random noise (even not visible to the human eye) to the blurred picture, and suddenly the "blur inversion" fails spectacularly
Does this actually work? I would have thought that, given the deconvolution step is just a linear operator with reasonable coefficients, adding a small amount of noise to the blurred image would just add similarly small amount of noise to the unblurred result.
To reconstruct the image one has to cut off those frequencies in the corrupted image where the signal to noise is poor. In many original images, the signal in high frequencies are sacrificable, so get rid of those and then invert.
https://en.wikipedia.org/wiki/Wiener_deconvolution
If one blindly inverts the linear blur transform then yes, the reconstruction would usually be a complete unrecognisable mess because the inverse operator is going to dramatically boost the noise as well.
Those unblurring methods look "amazing" like that but they are just very fragile, add even a modicum of noise to the blurred image and the deblurring will almost certainly completely fail, this is well-known in signal-processing
Not necessarily.
If, however, one just blindly uses the (generalized)inverse of the point-spread function, then you are absolutely correct for the common point-spread functions that we encounter in practice (usually very poorly conditioned).
One way to deal with this is to cut off those frequencies where the signal to noise in that frequency bin is poor. This however requires some knowledge about the spectrum of the noise and signal. Weiner filter uses that knowledge to work out an optimal filter.
https://en.wikipedia.org/wiki/Wiener_deconvolution
If one doesn't know about the statistics of the noise, not about the point-spread function, then it gets harder and you are in the territory of blind deconvolution.
So just a word of warning, if you a relying only on sprinkling a little noise in blurred images to save yourself, you are on very, very dangerous ground.