Support complex-valued decomposition on analytic signal to account for lagged signals

[tsalo]

Summary

I've been thinking about lagged signals (e.g., systemic low-frequency oscillations) and how tedana might account for them. I wonder if we could incorporate a decomposition method that supports complex-valued data (e.g., complex PCA and/or complex ICA) to decompose the optimally combined data into components that might have lags?

Just to clarify, this wouldn't be applied to complex-valued fMRI data (i.e., fMRI data with magnitude and phase reconstruction enabled)- it would involve a Hilbert transform on the magnitude-only optimally-combined signal.

Additional Detail

Tong, Hocke, & Frederick (2019) discuss systemic low-frequency oscillations (sLFOs), which are slow-moving waves stemming from non-neuronal sources. These waves move slowly enough that methods that don't take that into account (e.g., GSR) will average over those lags, blurring the extracted signal. Blaise Frederick developed the tool rapidtide to perform dynamic global signal regression.

More recently, Bolt et al. (2022) and Bolt et al. (2023) applied complex-valued PCA (code available at tsb46/complex_pca) to fMRI data to investigate the impact of sLFOs on global signal as well.

Scikit-learn's implementation of FastICA doesn't support complex-valued data, unfortunately, but I came across a repo that ostensibly extends FastICA to complex data (https://github.com/afbujan/complex_ica).

Between the Tong and Bolt papers, it seems like most (if not all) slow-moving signals in fMRI data are both non-neuronal and BOLD-based, in which case tedana couldn't flag them as noise (at least using TE-[in]dependence models). That might limit the utility of this approach within tedana, but I think it could still be useful for the blind source separation. We might end up with more "Likely BOLD" components, even if they're fundamentally non-neuronal, but I think they'd better represent the underlying signals.