[Mne_analysis] Noise estimation in EEG

[Matti Hamalainen]

Hi Octavian,

On Nov 24, 2012, at 9:47 AM, octavian lie wrote:

> Dear All,
>  
> Here is a fundamental question that has been answered in a conflicting way, related to EEG spike or ERP analysis.
>  
> When estimating the noice covariance matrix C of an EEG (data matrix nxt, n=no of electrodes, t=time), should one chose the identity matrix (no assumptions of the brain and measurement noise) or the one calculated on baseline pre spike/prestim epoch? Some think that for EEG, as opposed to MEG, estimating noise is not a good idea, whereas others think it should be ok. (this in the contexs of gaussian and noncorrelation assumption about noise).
> Also, if I should calculate the noise covariance matrix, since I am working with average spikes (calculated from a known no of individual, raw, spikes), should I correct in any way the noise covariance matrix by the no of spikes, and if yes, how do I do it?

Estimating noise is always a good idea, both for MEG and EEG. If MEG and EEG are combined, it is even mandatory to get the relative weighting of the two measures correct.
However, I am assuming on the basis of your email that you are interested in estimating sources on the basis of EEG only. 

Here are some hopefully useful points:

1. If evoked responses are analyzed, the conventional wisdom is to use baseline periods, i.e., portions of the data void of signals of interest. This same approach applies to EEG as well. If there is not enough such baseline data to yield a reliable estimate of the full spatial covariance, it is possible to omit the off-diagonal elements of the noise covariance when the MNE inverse operator is computed (--diagnoise option). In other words, when using --diagnoise we assume that the noise is not correlated between sensors but each sensor has a different noise variance (heteroscedastic noise).

2. If ongoing brain activity (not epileptic spikes) is analyzed, the MEG noise covariance is best estimated from the empty room data, i.e., from a recording in the absence of a subject. The problem here for EEG is that there is no such thing as an empty room measurement because the electrodes need to be connected to a subject and it is impossible to turn the brain off completely. However, we know that the "device" noise in the EEG channels should be uncorrelated across channels with some variations in the variance across channels. One might, therefore, compute the EEG "empty room" noise covariance from human data in eyes open condition with no stimulus or task and use the --diagnoise option. This results in heteroscedastic noise being overestimated but I think this is about the best we can do.

3. For epileptic spikes one can often safely assume that combined duration of the spikes is only a very small fraction of the total duration of the raw recording. Therefore, a reasonable noise covariance matrix estimate can be obtained by just using all the available data. I cc this to Naoro (Dr. Naoaki Tanaka) who might want to comment on this part.

I hope this helps.

- Matti

 


---------

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

msh at nmr.mgh.harvard.edu
mhamalainen at partners.org






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