I did look at this. It seems pretty coarse though -- wavelets generally divide the spectrum into power-of-two frequency bands, and the Gimp is no exception it seems. Also of course you have to remove all higher-frequency bands as well, since the halftone dots have high frequency content at the edges of the dots.
Trying it out now, I'm able to get a good result (to my eye) by deleting the top two bands, but it looks nearly identical to the article's blurring example.
Upscaling the image first by 141% and deleting the same two bands, the dots start peeking through, but the result looks closer to the article's inverse FFT result -- minus the artificial edge contrast enhancement that came from the author's use of black (rather than grey) circles.
G'MIC (which is available as a gimp plugin) has the exact same reversible fourier transform as a layer in it as the Fiji software he referenced. You can do the exact same operations from the article (or any other edits/blurs/selections to the peaks).
It's a bit cumbersome since you can't preview what you're doing, but quite workable. Was trying it out on his reference image this evening and got (IMO nicer) results fiddling with magic wand/fuzzy select/grow/shrink and various fills.
Trying it out now, I'm able to get a good result (to my eye) by deleting the top two bands, but it looks nearly identical to the article's blurring example.
Upscaling the image first by 141% and deleting the same two bands, the dots start peeking through, but the result looks closer to the article's inverse FFT result -- minus the artificial edge contrast enhancement that came from the author's use of black (rather than grey) circles.