Hi there,
I've started looking into the feat5 source code in more detail to port its pre-whitening routine to my own scripts and stumbled upon more questions (see below). Sorry if these are trivial or just blatantly wrong, but think they will help me better understand algorithm behind FSL's pre-whitening:
1) Based on paper and on comments in code seems like steps to take (for pre-whitening) are:
1. Fit regular OLS using data and design (am assuming here we want already temporally filtered (i.e., bandpass filtered) data and DM right?)
2. Take residuals from (1) and use them to compute an estimate to the autocorrelation. Seems like FSL code does this in spectral domain (which is more efficient) - so something like compute PSD and then take IFFT or that to get autocorrelation function?
3. Apply some regularization to estimate in (2) - in paper this is a Tukey taper + some spatial smoothing. Am wondering though where exactly in scripts this shows up?
4. Compute our pre-whitening matrix S by taking inverse of Cholesky decomposition of our autocorrelation estimate - i..e, Chol(V) = KK^\top and we want S = K^{-1}
5. Apply this pre-whitening matrix S to both data and design and re-fit model. This procedure can be repeated multiple times but, in practice, we only wish to do it once to avoid overfitting and wasted compute time (for similar results).
Thus far, most of info I gathered on this procedure (in source code) is on feat_model.cc, featlib.cc and prewritten.cc. Are there other scripts that also perform pieces of the pre-whitening routine I should take a look into? This info would save me a ton of time and make my code reading a bit more focused ;-)
Thank you so much for all the help!
Daniela
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