2 Preprocessing of EEG
21
with only limited information. Below we present several basic methods from both
groups that have been most widely used in EEG studies.
2.3.2.1 Linear Regression
Assuming that artifact reference channels are available and contain thorough waveforms of artifacts, linear regression has been one of the main vehicles used to cancel
artifacts from the EEG signal due to its simplicity and ease-of-use. A basic procedure is to estimate a portion of EEG contaminated by artifacts using regression and
to subtract the regressed portion from the contaminated EEG [22, 23, 45]. Linear
regression assumes that an EEG signal is the sum of an original brain signal and
a fraction of the artifact represented in reference. It estimates this fractional factor
from both the observed EEG signal and reference channel. The major drawbacks
of linear regression are that one or more reference channels must be available (e.g.
EOG or ECG), that it assumes a linear combination of EEG and artifacts where the
EEG signal may possess internal nonlinear dynamics and non-stationary, and that
it only applies well to a few types of artifacts such as EOG and ECG. However,
if reference channels are available, linear regression is still an effective solution to
remove artifacts [36, 107].
Linear regression methods operate particularly well with ocular artifacts since
EOG can be directly measured or indirectly inferred from EEG [13, 42]. However,
simple subtraction of a regressed portion of ocular artifacts from EEG can also take
out cerebral components. This problem is termed bidirectional contamination [91].
Many methods have been proposed to address bidirectional contamination among
which the aligned-artifact average procedure demonstrates promising results of canceling artifacts from eye movements or blinks while minimizing EEG contamination
[21–23].
2.3.2.2 Filtering
Filters used for artifact removal build a statistical machine whose parameters are
adaptively estimated with certain objectives, learning rules, model structures as well
as data. Three types of filters have been primarily adopted for EEG artifact removal
[104].
Adaptive filters model the way artifacts contaminate the EEG signal by adjusting
the filter weights according to a learning rule formed by an optimization algorithm
[47]. They assume no correlation between the EEG signal and artifacts. For example,
let x[n] be an observed EEG signal mixed with an unknown clean EEG signal y[n]
and an additive artifact signal z[n] (i.e. x[n] y[n] + z[n]). If the reference to artifact,
r[n], is available, the adaptive filter adjusts its weights, w, to minimize error between
x[n] and w
T r[n]. Since r[n] is assumed to be uncorrelated with y[n], the optimal
weights would make w
T r[n] as close to z[n] as possible. Then, a difference, {x[n] −
w
T r[n]} will become close to y[n] (Fig. 2.2). Many learning algorithms are available
21
with only limited information. Below we present several basic methods from both
groups that have been most widely used in EEG studies.
2.3.2.1 Linear Regression
Assuming that artifact reference channels are available and contain thorough waveforms of artifacts, linear regression has been one of the main vehicles used to cancel
artifacts from the EEG signal due to its simplicity and ease-of-use. A basic procedure is to estimate a portion of EEG contaminated by artifacts using regression and
to subtract the regressed portion from the contaminated EEG [22, 23, 45]. Linear
regression assumes that an EEG signal is the sum of an original brain signal and
a fraction of the artifact represented in reference. It estimates this fractional factor
from both the observed EEG signal and reference channel. The major drawbacks
of linear regression are that one or more reference channels must be available (e.g.
EOG or ECG), that it assumes a linear combination of EEG and artifacts where the
EEG signal may possess internal nonlinear dynamics and non-stationary, and that
it only applies well to a few types of artifacts such as EOG and ECG. However,
if reference channels are available, linear regression is still an effective solution to
remove artifacts [36, 107].
Linear regression methods operate particularly well with ocular artifacts since
EOG can be directly measured or indirectly inferred from EEG [13, 42]. However,
simple subtraction of a regressed portion of ocular artifacts from EEG can also take
out cerebral components. This problem is termed bidirectional contamination [91].
Many methods have been proposed to address bidirectional contamination among
which the aligned-artifact average procedure demonstrates promising results of canceling artifacts from eye movements or blinks while minimizing EEG contamination
[21–23].
2.3.2.2 Filtering
Filters used for artifact removal build a statistical machine whose parameters are
adaptively estimated with certain objectives, learning rules, model structures as well
as data. Three types of filters have been primarily adopted for EEG artifact removal
[104].
Adaptive filters model the way artifacts contaminate the EEG signal by adjusting
the filter weights according to a learning rule formed by an optimization algorithm
[47]. They assume no correlation between the EEG signal and artifacts. For example,
let x[n] be an observed EEG signal mixed with an unknown clean EEG signal y[n]
and an additive artifact signal z[n] (i.e. x[n] y[n] + z[n]). If the reference to artifact,
r[n], is available, the adaptive filter adjusts its weights, w, to minimize error between
x[n] and w
T r[n]. Since r[n] is assumed to be uncorrelated with y[n], the optimal
weights would make w
T r[n] as close to z[n] as possible. Then, a difference, {x[n] −
w
T r[n]} will become close to y[n] (Fig. 2.2). Many learning algorithms are available