Aggressive vs nonaggressive denoising

[dvsmith]

Thanks for the helpful clarifications. I had some related questions on a different thread that might haven gotten buried (ICA AROMA agg vs non-agg - #11 by dvsmith):

@dvsmith

1. With the non-aggressive denoising, we are basically using a matrix that contains both signal and noise, and we are saying that any shared variance between signal and noise will not be removed. But, if there is shared variance between columns that are denoted as “noise” (e.g., perhaps a CSF regressor is highly collinear with a white regressor and the motion parameters), then the shared variance here would be removed (because it is just noise anyway)? Is that correct?
2. Assuming I am on the right track with how I’m thinking about the non-aggressive denoising, I am curious how this would play out in the analyses. For example, if we have stimulus-correlated head motion, then it would probably not be removed in the case of non-aggressive denoising? Would this then bias our stats/inferences? It seems like the motion parameters would need to be included in the analysis to prevent this from happening, but would their inclusion lead to the reintroduction of noise that was removed earlier?