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".
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).
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.
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.
Except the size of the blocked section ofc. E.g If you know it's a person's name, from a fixed list of people, well "Huckleberry" and "Tom" are very different lengths.
JPEG compression can only move information at most 16px away, because it works on 8x8 pixel blocks, on a 2x down-sampled version of the chroma channels of the image (at least the most common form of it does)
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.
Enhance really refers to combining multiple images. (stacking) Each pixel in a low res image was a kernel over the same high res image. So undoing a 100 pixel blur is equivalent to combining 10,000 images for 100x super resolution.
The reason the filters used in the post are easily reversible is because none of them are binomial (i.e. the discrete equivalent of a gaussian blur). A binomial blur uses the coefficients of a row of Pascal's triangle, and thus is what you get when you repeatedly average each pixel with its neighbor (in 1D).
When you do, the information at the Nyquist frequency is removed entirely, because a signal of the form "-1, +1, -1, +1, ..." ends up blurred _exactly_ into "0, 0, 0, 0...".
All the other blur filters, in particular the moving average, are just poorly conceived. They filter out the middle frequencies the most, not the highest ones. It's equivalent to doing a bandpass filter and then subtracting that from the original image.
Here's an interactive notebook that explains this in the context of time series. One important point is that the "look" that people associate with "scientific data series" is actually an artifact of moving averages. If a proper filter is used, the blurryness of the signal is evident. https://observablehq.com/d/a51954c61a72e1ef
Emphasis mine. Quote from the beginning of the article.
This isn't meant to be a textbook about blurring algorithms. It was supposed to be a demonstration of how what may seem destroyed to a causal viewer is recoverable by a simple process, intended to give the viewer some intuition that maybe blurring isn't such a good information destroyer after all.
Your post kind of comes off like criticizing someone for showing how easy it is to crack a Caesar cipher for not using AES-256. But the whole point was to be accessible, and to introduce the idea that just because it looks unreadable doesn't mean it's not very easy to recover. No, it's not a mistake to be using the Caesar cipher for the initial introduction. Or a dead-simple one-dimensional blurring algorithm.
Other than that, you're not wrong about theoretical Gaussian filters with infinite windows over infinite data, but this has little to do with the scenario in the article. That's about the information that leaks when you have a finite window with a discrete step and start at a well-defined boundary.
FWIW, this does not read as constructive.
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.