source localizing frequency bands

✉️ Mailing List Archive (read-only)
1

Hi Gus,
  Your intuition that all the estimates should be similar is correct when
is no noise. But when there is noise, we have to go back to the math and
see what the sources you are looking at actually represent for each of
the different kinds of estimates (MNE,MCE, dipole fits, DICS etc.). This
is exactly the reason why filtering ahead is different from filtering
the MNE solution: The noise which one is trying to avoid when estimating
the sources is different in the 2 cases though the underlying 10Hz alpha
might be the same.

Regards,
Hari

2

Hari,

That makes sense. In other words, the better way to do this would be
to calculate the noise covariance with unfiltered data, and also do
source localization with unfiltered data. Then, look for sources that
have the oscillation of interest? Keep in mind that I'm talking about
raw data, and not averaged responses. Also, noise covariance would be
estimated with empty room measurements (or subjecting relaxing, but
regardless, raw data).

And that brings up another question. Based on this discussion, any
type of band-pass filtering of the data (be it to single out a narrow
band, or to filter out likely noise - e.g .1 to 40Hz filtering)
introduces temporal correlation to the noise, which hurts MNE
estimates because of its initial assumptions. In that case, would you
say that making estimates based on the signal prior to any filtering
is the safest thing to do?

Thanks,

Gus

3

Hi Gus,
   The noise covariance should ideally be the covariance of whatever is
considered as noise in the signal that you are applying the inverse
operator on. For example, if you are filtering the data between 0.1 and
40Hz and using empty room to calculate the noise covariance, you should
also filter your empty room between 0.1 and 40Hz. This is because the
signal on which you are going to use the inverse operator has noise
only in the 0.1-40Hz range.

It is true that this or any other filtering will cause noise to be
correlated in time (which it anyway might be), but its usually considered
OK unless the filtering is very extensive such as say 7-12Hz for alpha. Of
course there is no one best way to do this. That noise is uncorrelated in
time is a required assumption for MNE which may or may not hold depending
on what the noise is. My take would be to just not violate it extremely.

The other thing to keep in mind is that filtering can change your SNR and
that has strong effects on the MNE estimates. For example, if there is
some artifact at 50-55 Hz, filtering between 0.1-40Hz will improve the SNR
a lot and that should be recognized when calculating the inverse operator
and the inverse solution.

Hope that helps.

Regards,
Hari

4

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

5

Hi Matti,

Thank you for clarifying these issues. I thought I would take this
opportunity to ask a related question.

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.

By corollary, would you recommend filtering the empty room data to very
low frequencies (< 1 Hz, say) before computing the noise covariance matrix
if that happens to be the band of interest?

Pavan

6

Hi Pavan,

I meant filtering the very low frequencies *out*, i.e., setting the
pass band to, e.g, 1 - 40 Hz.

- Matti

7

Hi Matti,

By corollary, would you recommend filtering the empty room data to
very
low frequencies (< 1 Hz, say) before computing the noise covariance
matrix
if that happens to be the band of interest?

Hi Pavan,

I meant filtering the very low frequencies *out*, i.e., setting the
pass band to, e.g, 1 - 40 Hz.

- Matti

That was clear! I meant to ask the following question (sorry for the lack
of clarity). If one is interested in source localization of 'DC
fluctuations (0-1 Hz)', would you recommend filtering the emptyroom data
to 0-1 Hz prior to computing noise covariance?

thanks,
pavan