When using minimum norm methods for source estimation (in the case of EEG), which is to say going from the signal at the recording sites on the scalp to the signals in source space, i.e. equivalent dipoles for instance in an idealized cortical surface, a noise covariance matrix is often needed.

First of all, how is it computed? From what I have read, for instance in the MNE-Python package (source), the data is epoched into equal length segments, then the "covariance is computed". What is the precise mathematical formula applied to those epochs?

Second of all, this covariance matrix is said to be a measure of the reliability of the sensors. Why is that?

  • $\begingroup$ Can you clarify a bit which parts you do and do not understand? E.g., are you familiar with the concept of a "covariance matrix" overall? It also might be useful to provide a particular reference, as sometimes a noise covariance matrix comes from a measurement of true noise, like in an empty room, and in other cases "noise" means "background brain activity" which is some peoples' signal but other peoples' noise. $\endgroup$
    – Bryan Krause
    Nov 29, 2023 at 16:32
  • $\begingroup$ @BryanKrause I am familiar with the concept of the covariance matrix of two random vectors, so I have no issues conceptualizing it as each element in it being the covariance between two channels. Is this what is happening? If it is, how is the choice of a duration and overlap for the epoching justified? $\endgroup$
    – David Cian
    Nov 29, 2023 at 16:38
  • $\begingroup$ @BryanKrause As for the raw data, let's assume it's background brain activity, since I mentioned EEG, but I don't think the part about the interpretation of it as a measure of reliability would have a different explanation if talking about MEG and empty room measurements, would it? $\endgroup$
    – David Cian
    Nov 29, 2023 at 16:40
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    $\begingroup$ Thank you for your patience, I had opened the link, saw that it went past the abstract and, assuming the full text had loaded, did a search on the page for "reliability" and found nothing; however, the full text had not loaded so I missed it. My intuition is that they are using this word very imprecisely; the important takeaway is that a reasonable decision would be to minimize eq 13 (which is a scalar). In this context, it seems they're considering noise to be an additive voltage which would mean channels with more variance have more information on top of that additive voltage noise. $\endgroup$
    – Bryan Krause
    Dec 1, 2023 at 15:21
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    $\begingroup$ It also doesn't seem like Cd is actually a "noise covariance matrix" at all. $\endgroup$
    – Bryan Krause
    Dec 1, 2023 at 15:51


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