Information Technology Reference
In-Depth Information
X
x
¼
w
i
x
i
¼
wX
ð
7
:
1
Þ
i
x
with
filtered signal,
x
i
the EEG signal from channel
i
,
w
i
the weight
given to that channel in the spatial
the spatially
filter, and
X
a matrix whose
i
ith row is
x
i
, i.e.,
X
is
the matrix of EEG signals from all channels.
It should be noted that spatial
filtering is useful not only because it reduces the
dimension from many EEG channels to a few spatially filtered signals (we typically
use much less spatial
filters than original channels), but also because it has a
neurophysiological meaning. Indeed, with EEG, the signals measured on the sur-
face of the scalp are a blurred image of the signals originating from within the brain.
In other words, due to the smearing effect of the skull and brain (a.k.a., volume
conduction effect), the underlying brain signal is spread over several EEG channels.
Therefore, spatial
filtering can help recovering this original signal by gathering the
relevant information that is spread over different channels.
There are different ways to de
ne spatial
filters. In particular, the weights
w
i
can
be
fixed in advance, generally according to neurophysiological knowledge, or they
can be data driven, that is, optimized on training data. Among the
fixed spatial
filters, we can notably mention the bipolar and Laplacian which are local spatial
filters that try to locally reduce the smearing effect and some of the background
noise (McFarland et al.
1997
). A bipolar
filter is de
ned as the difference between
two neighboring channels, while a Laplacian
ned as 4 times the value of
a central channel minus the values of the four channels around. For instance, a
bipolar
filter is de
filter over channel C3 would be de
ned as
C3
bipolar
¼
FC3
CP3
, while a
Laplacian
filter over C3 would be de
ned as
C3
Laplacian
¼
4C3
FC3
C5
C1
CP3
, see also Fig.
7.4
. Extracting features from bipolar or Laplacian spatial
filters rather than from the single corresponding electrodes has been shown to
signi
cation performances (McFarland et al.
1997
). An
inverse solution is another kind of fixed spatial filter (Michel et al.
2004
; Baillet
et al.
2001
). Inverse solutions are algorithms that enable to estimate the signals
originating from sources within the brain based on the measurements taken from the
scalp. In other words, inverse solutions enable us to look into the activity of speci
cantly increase classi
c
brain regions. A word of caution though: Inverse solutions do not provide more
information than what is already available in scalp EEG signals. As such, using
inverse solutions will NOT make a noninvasive BCI as accurate and ef
cient as an
invasive one. However, by focusing on some speci
c brain areas, inverse solutions
can contribute to reducing background noise, the smearing effect and irrelevant
information originating from other areas. As such, it has been shown than extracting
features from the signals spatially
filtered using inverse solutions (i.e., from the
sources within the brain) leads to higher classi
cation performances than extracting
features directly from scalp EEG signals (Besserve et al.
2011
; Noirhomme et al.
2008
). In general, using inverse solutions has been shown to lead to high classi-
fication performances (Congedo et al.
2006
; Lotte et al.
2009b
; Qin et al.
2004
;
Kamousi et al.
2005
; Grosse-Wentrup et al.
2005
). It should be noted that since the
