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

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.