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waveform and the scalp spatial pattern of the intracranial dipolar current responsible
for the observed EEG,
city of the signal
received from the electrodes on the scalp. This chapter begins with a short review of
brain volume conduction theory, demonstrating that BSS modeling is grounded on
current physiological knowledge. We then illustrate a general BSS scheme
requiring the estimation of second-order statistics (SOS) only. A simple and effi-
increasing the sensitivity and speci
-
cient implementation based on the approximate joint diagonalization of covariance
matrices (AJDC) is described. The method operates in the same way in the time or
frequency domain (or both at the same time) and is capable of modeling explicitly
physiological and experimental source of variations with remarkable
flexibility.
Finally, we provide a speci
c example illustrating the analysis of a new experi-
mental study on error-related potentials.
The AJDC method for EEG data has been reviewed and described in details in
Congedo et al. (
2008
), based upon theoretical bases to be found in Pham (
2002
) and
Pham and Cardoso (
2001
). Typically, it has been used on continuously recorded
EEG (
spontaneous activity
, e.g., Van der Loo et al.
2007
). An extension of the
method to treat group EEG data and normative EEG data has been proposed in
Congedo et al. (
2010
). Such group BSS approach has been used in a clinical study
on obsessive-compulsive disorder in Kop
et al. (
2011
) and in a cognitive
study on spatial navigation in White et al. (
2012
). The AJDC method has also been
employed for motor imagery-based brain
ř
ivov
á
computer interfaces in Gouy-Pailler et al.
(
2010
), showing that it can be applied purposefully to event-related (de)synchro-
nization data (
induced activity
). Extension of the method to the analysis of
simultaneous multiple-subject EEG data is a current line of research in our labo-
ratory (Chatel-Goldman et al.
2013
; Congedo et al.
2011
,
2012
). This chapter
contributes demonstrating that the AJDC method can be used purposefully on
event-related potential (ERP) data as well (
evoked activity
).
-
8.2
Physiological Ground of BSS Modeling
It is well established that the generators of brain electric
fields recordable from the
scalp are macroscopic postsynaptic potentials created by assemblies of pyramidal
cells of the neocortex (Speckmann and Elger
2005
). Pyramidal cells are aligned and
oriented perpendicularly to the cortical surface. Their synchrony is possible thanks
to a dense net of local horizontal connections (mostly <1 mm). At recording dis-
tances larger than about three/four times the diameter of the synchronized assem-
blies, the resulting potential behaves as if it were produced by electric dipoles; all
higher terms of the multipole expansion vanish, and we obtain the often invoked
dipole approximation (Lopes Da Silva and Van Rotterdam
2005
; Nunez and
Srinivasan
2006
, Chap. 3). Three physical phenomena are important for the argu-
ments we advocate in this study. First, unless dipoles are moving, there is no
appreciable delay in the scalp sensor measurement (Lopes da Silva and Van
Rotterdam
2005
). Second,
in brain electric
fields,
there is no appreciable
