Simulate data with different parameters to show effects on ICA denoising

[tsalo]

I was thinking that we could probably simulate data with specific parameters, using real data as a basis. If we have (1) TE-(in)dependence model fit maps, (2) component weight maps, (3) component time series, and (4) variance explained maps, we could probably predict the multi-echo data for a range of echo times, numbers of echoes, etc. We could then run tedana on the simulated data to see how the various parameters impact the results.

[tsalo]

A few things to try varying:

1. Number of echoes from 3 to 8.
   • Do we expect low numbers of echoes to perform well? We certainly assume as much in Tedana.
2. Echo times from just covering the range of T2* values to 1.5x the max T2* value (see Logan's post here) to something far beyond that.
   • We could probably disable the adaptive mask to see if there's a problem with including bottomed-out echoes, and specifically to see what the nature of that problem is.
3. Lagged BOLD-based global signals (i.e., sLFOs).
   • Tedana, as it currently exists, shouldn't be able to do much with this. It should identify a temporally-blurred version of the global signal and accept it.
4. Localized task-related signals.
5. Spatially correlated BOLD and non-BOLD signals.
   • Tedana's spatial ICA shouldn't be able to handle this, so we might expect components that have both high Kappa and high Rho.
6. Temporally correlated BOLD and non-BOLD signals.
   • Tedana's spatial ICA should handle this successfully.
7. Motion-correlated non-BOLD signals.
8. Amount of thermal noise.
   • We can probably use the amount of variance removed by the PCA for this.
9. Patterns of thermal noise.
   • Does the scale of the thermal noise vary by echo? I assume so.
   • Does the time series of the thermal noise to vary by echo?