[Mne_analysis] source localizing frequency bands

[Matti Hamalainen]

Hi All,

Let me throw a few cents to this excitingly convoluted discussion.

Let's leave temporal correlations alone first.

If Y is the channels x times measurement data, the MNE is

X = WY

where W is the inverse operator. W depends on

A	the forward solution
R 	the source covariance matrix
C 	the noise covariance matrix estimate

The regularization parameter lambda basically determines the size of R  
as compared to the size of C.

*Any* filtering procedure (not just FIR) and also FFT means a  
multiplication from the right:

W(YF) = (WY)F = XF

so that it does not matter whether we we filter or compute the FFT  
before or after computing the MNE as long as A, R, and C stay the same.
It is of course, important that you work on the (signed) current  
component normal to the cortex or with the three current components  
without taking the absolute value or the length of the vector. Whether  
it is best to do the filtering before or after applying the inverse  
operator depends on the computational convenience.

Next comes the computation of the noise covariance. When spontaneous  
data are analyzed, the noise covariance should be computed from the  
empty room data, not from the brain data and especially not brain data  
filtered to the desired frequency band. If the latter is done, the  
results will be very weird, especially for the alpha band because you  
will end up considering the signals around 10 Hz noise and they will  
be dampened.

If you are not interested in very low frequencies, I think the empty  
room highpass could be set to a higher value then 0.1 Hz, e.g., 1 or 2  
Hz to cut of the prominent low-frequency noise which will  not be in  
the band of interest anyway.

If the data are temporally correlated, the whole premise of the MNE is  
violated but dealing with it properly is complex. However, as a first  
approximation, the temporal correlation affects the noise-covariance  
matrix estimates so that the noise will be underestimated because the  
samples are redundant.

Hoping not to create more confusion,
Matti



---------

Matti Hamalainen, Ph.D.
Athinoula A. Martinos Center for Biomedical Imaging
Massachusetts General Hospital

msh at nmr.mgh.harvard.edu






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