I have 2 noise footprint (one experimental and one obtained with numerical simulation), expressed as:
f1(x,y) and f2(x,y) with f1,2 complexes.
Which are the best metrics to estimate the degree of similitude between simulation and experiment?
RMSD seems the most easy choice:
Sqrt ( Int ( || f1(x,y) - f2(x,y)|| dxdy ) )
(although probably we are talking about a discrete sample, so the Integral is actually a Sum)
But maybe this solution is too easy: are there some particular "difference features" that you need to identify/enhance.
I'm not sure that "Noise" here has the meaning of "Random Noise".
Tell me if I'm wrong , but I think that here we are dealing with a spatial function describing the intensity of "sound" emitted by a source like an engine (called with an abuse of language "noise").
If on the contrary Noise is actually Random Noise, Yuriy Pilgun reply is correct: some statistical or spectral measure is more adequate.
Yes, Andrea is correct. Noise is not to be intended as disturbance, but as sound (unpleasant) produced by something. In this sense, the measure expressed by f(x,y) may be the amplitude and phase of a particular frequency in x,y point of a 2D space (i.e. ground) or a measure of total acoustic pressure (Overall Sound Pressure Level) in the same point. It is usually characterized in terms of intensity and directivity (referred to the source location) which may be particularly irregular and then RMSD may be misleading, since with a little rotation or translation an almost perfectly matching map may become a really bad one. I was wondering if some metrics involving Cross-correlation may be of help.
The problem could be resolved with an optimization of the relative orientation of the two reference systems, by minimizing the RMSD itself. So the "distance" is the minimum RMSD as a function of relative roto-translations.In a 2D system it should be pretty straight-forward.
But since the functions are in the complex domain and the two component are intensity and phase probably it would be better to fit the roto-trans using only intensity and then calculate the distance separately for phase and intensity, so using a 2-component distatnce? I don't know , I'm improvising.
By the way the roto-trans fitting is routinely made in other context as molecular modelling, were it is perfectly normal to compare two system (e.g. electrostatic potential of a protein and a mutant) after fitting one on the other by minimizing the RMSD of a subset of atomic positions.
My inclination here would be to do a spatial decomposition---perhaps of just the intensity---in terms of some basis (say spherical harmonics or 2D SVD) and compare the coefficients---again allowing for rotation and translation. That will make things a bit more robust and give you a better sense of the spatial scale where your model starts to breakdown.
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