Biomedical Engineering Reference
In-Depth Information
Scalp-recorded EEG
Independent components
EOG
1
Fz
2
ICA
finds an
unmixing
matrix,
Cz
3
Pz
4
W
Oz
5
T4
6
1s
1s
Activations
uWx
Scalp map
W
−
1
(a)
−
1
xWu
=
A
11
A
11
A
12
A
21
A
22
x
=
A
N1
Fz
A
11
A
12
A
21
A
22
Pz
x
=
proj
A
N1
(b)
Figure 2.7
Schematic overview of ICA applied to EEG data. (a) A matrix of EEG data,
x
, recorded at
multiple scalp sites (only six are shown), is used to train an ICA algorithm, which finds an “unmixing”
weight matrix
W
that minimizes the statistical dependence of the equal number of outputs,
u
Wx
(six are shown here). After training, ICA components consist of time series (the rows of
u
) giving the
time courses of activation of each component, plus fixed scalp topographies (the columns of
W
-1
) giv-
ing the projections of each component onto the scalp sensors. (b) The schematic illustration of the
back-projection of a selected component onto the scalp channels.
=
2.4.2.1 Assumptions of ICA Applied to EEG
Standard, so-called complete and instantaneous ICA algorithms are effective for
performing source separation in domains where: (1) the summation of different
source signals at the sensors is linear, (2) the propagation delays in the mixing
medium are negligible, (3) the sources are statistically independent, and (4) the
number of independent signal sources is the same as the number of sensors, meaning
that if we employ
N
sensors, the ICA algorithm we can separate
N
sources [24].
The first two assumptions above, that the underlying sources are mixed linearly
in the electrode recordings without appreciable delays, are assured by the biophys-
ics of volume conduction at EEG frequencies [40]. This is the basis for any type of
linear decomposition methods including those based on PCA. That is, the EEG mix-
ing process is fortunately linear, although the processes generating it may be highly
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