First, I'd like to apologize for my previous inaccurate reply: the rank of the scouts times series matrix is indeed linked with the number of sensors.
If you have Neeg=62 electrodes, the rank of your recordings is at most 62, or 61 if the data is in average reference and the recording reference is included. Additionally, the rank decreases for each SSP or ICA component that you remove during the signal cleaning.
Each source signal is a linear mix of the Neeg EEG signals. If you consider a set of more than 62 sources, the matrix [Nsources x Ntime] may have a rank up to Neeg. The scouts time series are averages of source time series, and would therefore share similar properties. When computing the signals associated with more than 62 scouts, the resulting matrix [Nscout x Ntime] may have a rank up to Neeg.
Limiting the number of scouts to 58 scouts would make it possible to obtain a "scouts matrix" [Nscouts x Ntime] that has a full rank. However, I'm not sure I understand this convoluted objective of computing scout signals and then orthogonalizing them:
- The orthogonalized signals would not have any correspondence with the underlying anatomical ROIs.
- Wouldn't you obtain similar signals as when processing the EEG signals directly? (minus the information that is lost during the inverse model computation - see regularization)
Working with volume sources would bring you closer to the pipeline you refer to, but then you would face a problem of having sources with unconstrained orientations (3 signals per ROI).
On the surface, the selection of the type of parcellation to be used is not trivial, and I don't know how to guide you with this. One recommendation I can give you is not to try using a volume parcellation (eg. AAL) for processing sources estimated on a surface.
As a software engineer, I am not competent to address these questions. I would recommend you seek advice from signal processing specialists.
@John_Mosher @Sylvain Can you please share your recommendations?
I was just a bit concerned that the downsampled atlas has somewhat of a patchy appearance.
Only vertices are classified as part of scouts, not faces. The faces between two ROIs are not attributed to one or the other and therefore not painted. Display the surface edges and zoom in to observe this.
Other threads discussing rank of source space signals: