Asking the right questions . See: Cleaning of scanned photo overlaid with pattern for more inspiration. There may be other threads.
It has also been discussed in the ImageMagick:
- docs http://www.imagemagick.org/Usage/fourier/#noise_removal
- and forums http://www.imagemagick.org/discourse-server/viewforum.php?f=1
Also, have you tried all of the existing filters? There are already some that use FFT which may fulfill your needs. Search: