Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 112

However the general nonuniqueness of source localization solutions and the poor
spatial resolution afforded by EEG data limit applicability of this approach [Achim
et al., 1991].
Among the methods, which do not rely on specific models is a class of blind
source separation algorithms (BSS), which includes PCA and ICA approaches (Sect.
3.6.1 and 3.6.2) They are based on the assumption that by projecting the data onto
orthogonal (PCA) or statistically independent components (ICA) the components
corresponding to artifacts can be isolated.
The rejection of all artifact contaminated epochs may result in severe loss of data.
Therefore methods for correcting the artifacts rather than only detecting the artifact
contaminated epochs were devised. They were based on filtering, regression analysis,
PCA, and more recently on ICA [Jung et al., 2000].
Simple filtering of signals to eliminate, e.g., muscle or ECG artifacts relies on
the assumption that the interesting part of EEG signal is expressed in a different
frequency band (usually lower) than the artifacts. However, the low-pass filtering
leads to excessive smoothing of data and usually disturbs the higher frequency EEG
rhythms.
The regression method is based on the assumptions that: 1) artifact activity may
be measured concurrently with EEG, 2) there is a linear relationship between EEG
and activity connected with the artifact source, 3) there is no temporal delay between
both signals. These assumptions are to a large degree valid for eye movements. The
algorithms for EOG artifact corrections were developed by [Gratton et al., 1983,
Semlitsch et al., 1986]. They are based on the mechanism of finding blink-affected
data epochs in the EOG channels. Then the regression of the eye channel(s) with
each individual EEG channel is performed. The corrected EEG cor series are given
by the formula:

EEG cor = EEG − w · EOG . (4.2)

where w is the regression weight for the given channel. There are several problems
connected with this approach discussed in [Croft et al., 2005]; the most important
one is connected with the fact that not only does EOG influence EEG, but also,
vice versa, EEG contributes to EOG signal. In the process of correction some EEG
activity is also removed. For this reason nowadays the methods based on ICA are
favored [Makeig et al., 1996, Delorme et al., 2007].
The procedure of finding the independent components was described in Sect.
3.6.2. For multichannel EEG or ERP the input matrix x (of k rows corresponding to
the sensors) is used to train the ICA algorithm, which estimates an unmixing matrix
D − 1 that minimizes statistical dependence of the outputs s . We can expect that the
activities generated by different sources, e.g., eye or muscle artifacts, will be isolated
as separate ICA components. Brain activities of interest can be obtained by project-
ing selected ICA components back on the scalp. In the process of back-projection
the components corresponding to artifacts can be eliminated by setting the corre-
sponding rows of the source matrix s to zero. In this way the corrected signals may
be obtained. However, one should keep in mind that the “unmixing” is usually not
perfect, and there may be some crosstalk between the components; thus in removing