I think Ronounours has already done an excellent recovery, here are some comments anyway
1./ re. why is FFT difficult inside GIMP
using fft and inverse fft must be with a floating point precision as the quantities produces are well outside the 0-255 values that 8-bits per channel can represent.
best way to play is with the command line but you can mess around in the "custom filter" and preview too.
2./ re. why is "anisotropic" good
We start by noticing that the screening frequencies and other noise seem to be mostly at high frequencies, so a first estimate of noise removal can be a low-pass or a blur but often that loses edge information too , by using anisotropic filters we can preserve edges, and it is another optimisation as to "how much"
sometimes it is nice to visualise the noise itself and instead recover edge data to put back into the image .. see under Testing / Iain Fergusson in GMIC menu for examples of "detail recovery".
In this case there is also a problem from JPEG compression quantizing values in Y'CbCr colourspace and 4:2:2 resolution which gives a lot of cross-talk in chroma noise from the original scan of CMYK printed material where there are four distinct grid orientations - see the "star" shape still visible in noise is actually in all channels - if we could start with an original uncompressed scan it might be that C M Y K split could be treated separately.
Anyway on my machine I ran this command line to get the image uploaded here ..
cd C:\msys\home\James\gmic-1.5.7.0\src
set PATH=c:\msys\bin;%PATH%
C:\msys\home\James\gmic-1.5.7.0\src>gmic.exe c:\Users\James\Pictures\20130904fft.jpg --b 5 --[0] [1] --smooth[0] 40,0.2,0.8 --[0] [2] -+[1,2] --fftpolar -rm[3,5] -log[2,3] -*[2,3] 15 -+[0] 127 -a[1,3] y -a[0,2] y -a[0,1] x -c 0,255Attachment:
File comment: a look as estimated noise and its spectrum
20130904-lowfreqplusedge-noiseest-andlogffts.jpg [ 98.69 KiB | Viewed 2496 times ]
Explanation of the steps:
--b 5 --[0] [1] # split high from low spatial frequency components
--smooth[0] 40,0.2,0.8 # recover some edge information from high component
--[0] [2] -+[1,2] # subtract and add to update original estimates
--fftpolar -rm[3,5] # visualise the power spectrum ignoring the phase
-log[2,3] -*[2,3] 15 -+[0] 127 # scaled log for fft and grain-extract for noise
-a[1,3] y -a[0,2] y -a[0,1] x -c 0,255 # combine all four into a big 8-bit image