[Mne_analysis] Derived measures and MNE

[Gregory Cogan]

Good afternoon everyone,
I've been having a discussion with a number of colleagues about computing
derived measures in sensor space and then computing the forward
model/inverse solution based on these values.  To give an example, say you
computed a cross correlation between some property of your stimulus (time
varying stimulus) and each sensor of MEG data (in time).

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).  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?

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.

Any insight would be appreciated,

Gregory B. Cogan
Postdoctoral Research Scientist
Center for Neural Science
New York University
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