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set to 0.05, meaning that the probability of falsely rejecting even only one
hypothesis is less than 0.05. All permutation tests were approximated by the use of
5,000 random permutations.
8.8.6 Analysis in the Source Space
As we have seen that a spatial
filter computes a weighted sum (linear combination)
of the signal obtained at each electrode, potentially isolating delimited dipolar
sources from each other. We apply here the method introduced above adapting it to
ERP data. Our goal is to separate the source of the Ne (ERP) and the source for the
theta ERS. We need to separate them one from the other, but also from background
EEG activity. For our purpose, we need to include in the diagonalization set
matrices holding (a) the spatial structure of the ERP component, (b) the spatial
structure of the ERS component, and (c) the spatial structure of the spontaneous
EEG oscillations and persistent artifacts such as lateral and horizontal eye move-
ments, jaw muscle contractions, etc. For (a) and (b), we compute the relevant
covariance matrices both on error trials and on correct trials so to exploit variations
of source energy between the two conditions (Table
8.1
). We de
ne an exactly
determined BSS model, that is to say, we estimate as many sources (
M
in the
formula above) as electrodes (
N
=
M
= 31). For the ERP components (a), we
estimate the covariance matrix of the average ERP in the three time windows where
the ERP analysis in the sensor space revealed signi
cant results (see next section).
Covariance matrices were separately computed for error and correct conditions,
providing 3
×
2 = 6 matrices.
These six matrices provide unique source energy
pro
le about ERP that have different potential in error versus correct trials
. For the
ERS component (b), we estimate the averaged covariance matrix in the time
-
fre-
quency region where the sensor space analysis revealed signi
cant results (see next
section). These matrices were computed as the covariance matrices of the EEG
filtered in the frequency band of interest. Again, matrices were computed separately
for error and correct conditions, providing two additional matrices.
These two
matrices provide unique source energy pro
le about ERS that display different
power in the theta band in error versus correct trials.
Notice that matrices for the
ERP and the ERS components are substantially different: For the ERP components,
EEG trials are averaged before computing the covariance matrix (thus only both
time-locked and phase-locked signals are preserved), while for the ERS compo-
nents, trials are averaged only after computing covariance matrices on single-trial
data (thus, non-phase-locked signals are preserved as long as they are time-locked).
To separate possible sources of ERP and ERS from spontaneous EEG oscillations
and artifacts (c), we include in the set all cospectral matrices (Bloomfield
2000
)of
the signal during the
20 Hz using a
frequency step of 2 Hz, providing 10 additional matrices.
These latter 10 matrices
provide unique source energy pro
fixation cross sequence in the frequency range 2
-
le to separate all spontaneous sources having
non
-
proportional power spectrum
(Table
8.1
). In summary, our BSS algorithm
