Quantitative EEG-Based Brain-Computer Interface - Quantitative EEG Analysis Methods and Clinical Applications - page 207

mu-band power around electrode C4 (over the corresponding cortex area of the left
hand). Accordingly, right-hand imagery causes a similar mu-band power decrease
on electrode C3. This makes it possible for a classifier to discriminate the states of
left- or right-hand motor imagery just by using spatial distribution of mu-band
power.
Another SMR-based BCI approach proposed by Wolpaw et al. was to train the
users to regulate the amplitude of mu and/or beta rhythms to realize two-dimen-
sional control of cursor movement [12]. Two linear equations were used to trans-
form the sum and the difference of EEG power over left and right motor areas into
vertical and horizontal movement of screen cursors.

8.3.2 Spatial Filter for SMR Feature Enhancing
In SMR-based BCI, localized spatial distribution of SMR is a crucial feature other
than its temporal power change. Because EEG has very poor spatial resolution due
to volume conduction, constructing virtual EEG channels using a weighted combi-
nation of original EEG recordings is a commonly used technique to get a clear local
EEG activity, or “source activity” [21, 52]. The general idea of spatial filtering can
be denoted by the following equation:

YFX =⋅ (8.5)

where X is the original EEG data matrix, containing recordings from each electrode
in its rows; and F is a square transformation matrix to project the original recordings
to virtual channels in the new data matrix Y .Eachrowin Y , as a virtual channel, is a
weighted combination of all (or part of) the original recordings. The filtered data
matrix Y is supposed to be better than X , for extraction of task-related features.
So far, for SMR signal enhancement, two categories of spatial filters have been
explored. One category is based on EEG electrode placement, such as common
average reference (CAR) and Laplacian methods [53]. CAR virtual channels are
obtained by subtracting the average signal across all EEG electrodes from each orig-
inal channel, as shown in the following formula of weighted combination:

1

n

= ∑

CAR ER ER

VV n = − Vi = 1 , , n (8.6)

i i j

j 1

where n is the number of electrodes and V i ER is the original EEG recording. Simi-
larly, the Laplacian channels are constructed by removing contributions of neigh-
boring electrodes from the central electrode as follows:

∑

LAP ER ER

VV = − g V

i i ij j

jS ∈

(8.7)

i

( )

( )

∑

g = 1 d 1 d

ij ij ik

kS ∈ i

where S i is a subset of neighboring electrodes of the i th electrode and d ij denotes the
geometric distance between electrode i and electrode j. If S i consists of the near-