Brain–Computer Interfaces - Index of

Digital Signal Processing and Machine Learning 309
yi = xi − 1
N (x1 +···+xN), (2)
where i = 1, ··· , N.
CAR is a linear transformation method in which all entries of the ith row of the
transformation matrix W in (1) are − 1
N−1 except that the ith entry is 1. The CAR
method is effective in reducing the noise that are common to all electrodes, such
as the interference of 50 or 60 Hz power sources. Since the useful brain signals are
generally localized in a few electrodes, this method enhances the useful brain signals
from the averaged signals. However, the CAR method is not effective in reducing
noise that are not common to all electrodes, such as electrooculogram (EOG) from
eye blinks and electromyogram (EMG) from musclclclcle contractions. The EOG
signal is stronger at the frontal cortex, and the EMG is stronger near the relevant
muscles. Therefore, other methods such as regression methods or ICA have to be
used to reduce these artifacts.
2.1.3 Laplacian Reference
Laplacian reference adjusts the signal at each electrode by subtracting the average
of the neighboring electrodes. The Laplacian method is effective in reducing noise
that should be more focused at a specific region. Here we describe two types of
Laplacian references: small and large. For example, Fig. 3 presents a 64 channel
electrode cap with small and large Laplacian references.
The small Laplacian reference subtracts the averaged EEG signals of the nearest
four electrodes from the signal being preprocessed as shown in the left subplot of
Fig. 3. In this example, the 9th preprocessed EEG signal (y9) computed using the
small Laplacian reference is given by
y9 = x9 − 1
4 [x2 + x8 + x10 + x16]. (3)
Fig. 3 Laplacian reference preprocessing for the 9th channel of EEG signal. Left: small Laplacian
reference. Right: large Laplacian reference