So how do we get rid of periodic noise? In the same manner as the filtering examples shown in the first post. The trick is identifying where the frequency is to be removed. Consider this image which shows a very prevalent periodic noise throughout the image. Any form of normal spatial filter would have a hard time removing this artifact.
Enter the FFT. The images below show the power spectrum of the image above before and after the frequency components responsible for the periodic noise have been filtered.
Now taking the inverse of the FFT results in an image with the periodic noise gone.
FFT helps isolate regular patterns in an image and remove them. Like magic!