Noise estimation in EEG

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?

Thank you,

Octavian.
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Hi Octavian,

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

Hi again,

Thank you very much,

Related to your points 1. Practically, is there a 250 ms prestim baseline
enough for a full covariance calculation instead of diagnoise. I suppose
this depends on the level of noise and the SNR at the time of interest, no
of epochs to be averaged. However, at the onset of analysis (again
involving average epileptic spikes in EEG), how much baseline in enough
(conventionally)?

                                  3. The question is whether to correct the
noise covariance matrix for the no of individual spikes that were averaged
or not. Again, the issue is that I have the averaged spike, but not the
original individual or raw spikes, however I know the number of spikes that
were used in averaging. From the MNE manual: "In the MNE software the
noise-covariance matrix is stored as the one applying to raw data. To
reflect the decrease of noise due to averaging, this matrix,C0 , is scaled
by the number of averages, L, i.e., C=C0/L."

An additional point. How do I calculate the SNR at timepoint of interest
(say peak of the spike) given a calculated noise covariance matrix? its
trace may give me the denominator, but how about the numerator (say I have
n electrodes, and a nxt data matrix (t=time), the noise covariance matrix
will be nxn. At time tj (corresponding say to the peak of spike), the data
will be a column vector nx1 at tj. )

Octavian

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