I don’t know where to start since this is information theory 101.
Not what I meant. Take matlab or python or whatever, generate a 2D ‘pixel’ grid and fill it with your favourite noise type. Then do a FFT, look at the spectrum of spatial frequencies. Does that plot contain just high frequencies? Remember: a fourier transform is ‘just’ switching the basis of how you represent your measurements. So if you want to, yes you certainly are in fourier space. That’s exactly why I chimed in, as I saw a…let’s say bold statement…regarding spatial frequencies (you changed the basis set in order to make that statement anyway) of noise.
Well. Noise is a random distortion of whatever you want to measure, however you sample it. Spatial frequencies may not be normalized to the unit of seconds but to whatever image dimension you want…picture height, block-size…but the same priciples apply. Take a photo of a flat surface at low light and do a FFT of the resulting image, you’ll see that the noise spectrum contains all frequencies at various intensity levels.
No. Take for example DCT-denoising or Wavelet denoising. They do coefficient shrinkage either in discrete cosine frequency domain, or in wavelet domain (which is a more complex change of basis set than a fourier transform, it’s multiscale by nature o the transform). nlmeans has problems with low frequency noise and that’s one of the reasons why multi-scale denoising schemes are investigated. Multiscale in order to attack not just high frequencies for algorithms that out of the box just chuck away high frequency detail.
The detail mask dicussed in here, is one of many tools in denoising to restrict effects to ‘flat’ areas. In terms of frequency, those are low-frequency. Leaving edges alone is very important because the fourier transform of an edge is…? You guessed right, broadband in spatial frequency terms. You have broadband noise, and broadband features and you need algorithms to distinguish random noise from real structure.
Of course the detail mask is good for many other things as well like we see in this thread (feature selective sharpening and local contrast adjustments).