[Mne_analysis] How is the Source Covariance matrix (R) calculated in the current estimate algorithm

[Hari Bharadwaj]

Hi,
  If you think of the MNE inverse solution in the Bayesian context, the
source covariance matrix is part of the "prior".. i.e., it is something
that is assumed based on previous knowledge..

The standard assumptions that are used that determine R are as follows:
(i) Apriori all sources are mean 0, and given equal weight to be active
and independent of each other: this means that R is a diagonal matrix with
all the elements on the diagonal being equal to the same number..

(ii) The SNR you get in your measurement is 3:1. This, along with the
estimate of the noise covariance matrix helps determine what that constant
on the diagonal ends up being..


If you have say a map of weights you want to give to the sources instead
of the above (say based on a prior fMRI experiment), then you would make
corresponding entries along the diagonal of R higher or lower to match
your prior.

HTH..

Hari




On Mon, June 2, 2014 1:21 pm, Thinh Nguyen wrote:
> Hi MNE users,
>
> I've recently spend a lot of time trying to understand the algorithm used
> in MNE software, majorly from this MNE link:
> http://martinos.org/mne/stable/manual/mne.html
> I'm having a hard time understanding how the Source Covariance matrix (R)
> is calculated, as the source is unknown. For example, these equations
> involved known R to calculate the inverse operator:
>
> [image: \tilde{M} = R \tilde{G}^T (\tilde{G} R \tilde{G}^T + I)^{-1}\ ,]
>
> [image: \tilde{M} = R^{^1/_2} V \Gamma U^T]
> It would be great if you can point me to literature references explaining
> this algorithm. Thank you in advance.
>
> Regards,
> Thinh Nguyen
> _______________________________________________
> Mne_analysis mailing list
> Mne_analysis at nmr.mgh.harvard.edu
> https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis


-- 
Hari Bharadwaj
PhD Candidate, Biomedical Engineering,
Boston University
677 Beacon St.,
Boston, MA 02215

Martinos Center for Biomedical Imaging,
Massachusetts General Hospital
149 Thirteenth Street,
Charlestown, MA 02129

hari at nmr.mgh.harvard.edu
Ph: 734-883-5954