ENH: add PCA-based motion correction for fNIRS (motion_correct_pca)

[leonardozaggia]

Reference issue (if any)

What does this implement/fix?

Adds motion_correct_pca (alias pca) to mne.preprocessing.nirs for
PCA-based motion correction of fNIRS data.

The function extracts motion-artifact segments, performs SVD across all
fNIRS channels, removes the dominant principal components explaining the
top nSV fraction of variance, and reinserts the cleaned segments.

Based on Homer3 v1.80.2 hmrR_MotionCorrectPCA (Huppert et al. 2009).

Returns the corrected Raw, the normalised singular values, and the number
of components removed.

Additional information

• Operates on optical density or hemoglobin data.
• nSV accepts a fraction (0 < nSV < 1) for variance-explained threshold
  or an integer for exact component count.
• This is one of three related PRs adding Homer3-based motion correction
  to mne.preprocessing.nirs:
  • PCA: this PR
  • Spline: ENH: add spline interpolation motion correction for fNIRS (motion_correct_spline) #13693
  • Wavelet: ENH: add wavelet-based motion correction for fNIRS (motion_correct_wavelet) #13692

[drammock]

For us to incorporate this, I think we would need explicit permission from a Homer3 maintainer to relicense (the Homer3 software license agreement looks custom, mostly the same as BSD-2 but with an extra paragraph at the end).

When we incorporate BSD-licensed code we typically add names and link to the donor project inline in the source file(s) where the adapted/translated code ends up.

@leonardozaggia can you tag someone here with relevant authority to give that permission?

[leonardozaggia]

@drammock thank you for the feedback! I think @dboas or @jayd1860 could help us with that.
I am now waiting to see if I should resubmit the nirs-motion-correctoin PRs to the dedicated mne-nirs dependency instead, as per discussed here: #13693