Sorry but this post is the blind leading the blind, pun intended. Allow me to explain, I have a DSP degree.

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