I don't understand why you come up with FFT Spectre, when I just explained why it won't work. :\
Fast Fourier Transform doesn't work on randompatterns like this and you'll only get the plain frequency output as shown in my example. You will get the same output in the red, green and blue channel.
Anyways, you might want to try median, which doesn't blur edges as much as Gaussian blur does. Since removing this pattern is not an easy job, you want to ask yourself if you really have to remove it. The point is that if your output is going to be a 8x12 print or smaller, then the pattern becomes less of a problem. It's only when you have really large prints that you immediately will notice the pattern, but then one could also say; are large prints intended to look at from really close?
The point I?m trying to make is that it?s pretty much impossible to remove the pattern without blurring some fine details (unless you like two spend a whole week on smudging, blurring and cloning and even then you need to have some painting skills) and you have to ask yourself if that?s worth it.
Sorry, I wish I had a better answer neville310, but there is no miracle solution for this one.