[Mne_analysis] Derived measures and MNE

[Alexandre Gramfort]

Hello Gregory,

sorry for the very response delay but HBM makes us quite busy.

> Would it be possible to compute the minimum norm solution based on these
> derived values instead of actual data?  To me, you could easily do this if
> you computed the entire MNE solution based on your actual data, and then
> computed the raw inverse on the cross correlations as this would be the
> equivalent of computing the cross correlations in source space (since it's a
> linear transformation).

correct. See:

https://github.com/mne-tools/mne-matlab/blob/master/matlab/mne_ex_compute_inverse.m

for a matlab function that explains how you could do this.

> Where it becomes unclear, is how you would/could
> compute it right from the start.  For instance, could you compute a noise
> covariance matrix based on the covariance of cross-correlations in a period
> of non-interest and a data covariance matrix of cross correlations within
> your period of interest?  Would this 1) be a meaningful construct and 2)
> adequately characterize the statistical properties of the data required to
> perform the minimum norm solution?

I don't feel that using a custom covariance for the quantity you're interested
is the most reasonable choice.

The covariance used for whitening comes from the model:

data = leadfield x sources + noise

What would be the model in your case?

> Matters get somewhat more confusing if you assume that the cross
> correlations presumably would be computed in a narrow band of interest, and
> so another question would be whether or not you would have to band pass your
> period of non-interest for your noise covariance matrix.

If the question is : should I use a covariance matrix per frequency band?
My answer is : some people do.

> Any insight would be appreciated,

hope this helps.

And sorry again for taking so long to answer.

Alex