Estimate magnitude and phase error variance for phase regression

[tsalo]

Per Curtis 2014, the fit of the phase regressor should be conditioned on the relative error levels in the measurements (magnitude and phase signal). A quote:

As a coarse measure, one can estimate the standard deviations σS and σφ of the magnitude and phase time series respectively, if the signal changes of interest can be factored out.

It looks like they did this in task data by performing a task-based regression using the convolved task signal and then estimating standard deviations from the residuals. With resting state data (as in Curtis 2014), they "removed" ostensible BOLD signal with a bandpass filter. I'm not a huge fan of incorporating task information in a preprocessing pipeline, and it's unclear to me if the regression is actually performed on the full data or just the residuals.

[tsalo]

Perhaps BOLD signal could be removed by regressing out volume-wise T2* estimates? That would include physiologically-based BOLD signal (i.e., non-neuronal BOLD noise), but I'm not sure if that's a problem.