I try to understand the noise covariance as implemented in Brainstorm. I am using the software for source localization of interictal spikes in pts with epilepsy. My analysis is done on a per subject basis. For each subject, I have 4 conditions, with a variable no (n1 to n4) of spikes per condition. I have access to raw EEG epochs (individual spikes), and averages/condition (imported, not calculated in BS). It is likely that in my case, the noise can vary a lot with time at each sensor- I am using long term EEG:
Should I caculate noise cov on concatenated individual spikes in a given condition, then use it for source imaging on the respective average for each condition, or should I calculate the noise cov directly on each average/condition?
There is the suggestion in Tutorials that if baseline time samples are limited, the use of individual trials/condition is a solution. How much time is … enough to decide between the two?
Related to the above, how long the prespike baseline should be … is there any data in the case of EEG? I think a published reference of the math of calculating the covariance would help.
What is the difference beween the full noise cov and the diagonal matrix ?
For the noise covariance concept: it's a matter of estimating the variance of the noise at each sensor. It helps conditioning the inverse model a little better, but it is valid only if you have data samples that represent noise fluctuations correctly. In MEG, the main source of noise is form the environment, hence we suggest to use some empty-room recordings to define the noise model. In EEG, there is nothing equivalent to empty room as the electrodes need to be positioned on the scalp so that the impedances are properly set. In event-related potentials, with multiple trials, the classic view is to consider pre-stim average brain activity as 'noise'. For single trial spike analysis as in your case, the brain activity before the spike is definitely not noise. Hence you don't want to bias the noise model you define. It is therefore safer not to inform the noise model and select 'identity' for the noise covariance matrix (equal, unit variance of noise on every sensor).
I'm forwarding the question to other specialists of epilepsy recordings to provide you with a better response.
Francois
I am curious to know how a spike and an individual ERP trial differ conceptionally when it comes about the noise consideration. This is important as sLORETA includes noise covariance in its estimations. As to the theory if noise covariance, I found a nice page on the MNE homepage. Thank you for forwarding this issue to Sylvain and EEG folks.
You’re fundamentally right: if one considers that there is no such thing as brain noise, there should be no difference in the modeling approach between an individual ERP response and an epileptic spike. There is a true issue with informing a noise-covariance model in EEG, with unaveraged, ongoing data.
As I think I mentioned elsewhere, in that case, it is probably better to assume no specific noise statistics except IID over all electrodes, i.e.: use an identity matrix as noise covariance model and discard noisy electrodes from the source model. For averaged ERPs, it’s different: prestim baseline data should do the job. A similar approach, computing noise covariance statistics away from the peak of an averaged interictal spike, is equivalently valid.
But for single-event data, EEG is problematic because one cannot capture instrumental noise as conveniently as with an empty-room recording with MEG.