24
S.-P. Kim
estimate of sources and a mixing matrix, thus, is achieved by certain assumptions
on the sources such that the sources are mutually independent or uncorrelated. For
instance, let x be an observed EEG signal vector, which is a mixture of an unknown
source vector s with a mixing matrix A, given by:
x As + n
(2.1)
where n denotes additive white noise.
Then, BSS methods estimate A to make sources in s as independent as possible.
Once the estimate of A is obtained, its inverse matrix W A
−1 is used to find the
sources given by:
s W x.
(2.2)
These estimated sources are then inspected either empirically (by visual inspection, for example) or automatically (by automatic source selection algorithms [109,
111, 119]) to identify artifact-related sources. The reduced set of sources after removing artifactual ones are then used to reconstruct artifact-free EEG data using A.
Despite its prevalence in EEG preprocessing, BSS suffers from limitations that it
requires multi-channel EEG data and that there is always a possibility that removed
sources may also carry information about brain activity. In addition, researchers
should take into consideration the assumptions each BSS method works under,
including independence, uncorrelatedness, and non-Gaussianity [54, 71]. A variety
of BSS methods, however, have been successfully applied to remove artifacts from
biomedical signals. Below are described several methods that have been widely used
for EEG artifact removal.
Independent component analysis (ICA) is a BSS method based on assumptions
of mutual linear independence between sources and non-Gaussianity [7]. ICA algorithms are based on either second-order or higher-order statistics [54]. The ICA
algorithms based on higher-order statistics estimate W by maximizing statistical
independence of the probability density functions of individual sources using mutual
information or negentropy [7, 19]. The ICA algorithms based on second-order statistics estimate W by decorrelating the time-series data using the second-order blind
identification (SOBI) [20, 103]. ICA has been reported to perform well in EEG artifact removal due to its reasonable assumption of statistical independence between the
EEG signals and artifacts (e.g. see [2]). However, to explore statistical independence,
ICA needs the sufficient amount of EEG data [56]. Also, ICA works best when the
artifacts and the EEG signals remain stationary during the period of analysis, which
may not be the case in general. To ensure stationarity, studies have suggested an
epoch of 10 s or less, or a sample size in the order of multiples of
√
C where C
is the number of channels [56, 92]. When only a limited number of data samples
are available, studies have suggested using the ICA algorithms with second-order
statistics [28, 55].
Principal component analysis (PCA) has been proposed as a means to remove
artifacts from EEG [39, 67, 102]. PCA transforms presumably correlated multi-
S.-P. Kim
estimate of sources and a mixing matrix, thus, is achieved by certain assumptions
on the sources such that the sources are mutually independent or uncorrelated. For
instance, let x be an observed EEG signal vector, which is a mixture of an unknown
source vector s with a mixing matrix A, given by:
x As + n
(2.1)
where n denotes additive white noise.
Then, BSS methods estimate A to make sources in s as independent as possible.
Once the estimate of A is obtained, its inverse matrix W A
−1 is used to find the
sources given by:
s W x.
(2.2)
These estimated sources are then inspected either empirically (by visual inspection, for example) or automatically (by automatic source selection algorithms [109,
111, 119]) to identify artifact-related sources. The reduced set of sources after removing artifactual ones are then used to reconstruct artifact-free EEG data using A.
Despite its prevalence in EEG preprocessing, BSS suffers from limitations that it
requires multi-channel EEG data and that there is always a possibility that removed
sources may also carry information about brain activity. In addition, researchers
should take into consideration the assumptions each BSS method works under,
including independence, uncorrelatedness, and non-Gaussianity [54, 71]. A variety
of BSS methods, however, have been successfully applied to remove artifacts from
biomedical signals. Below are described several methods that have been widely used
for EEG artifact removal.
Independent component analysis (ICA) is a BSS method based on assumptions
of mutual linear independence between sources and non-Gaussianity [7]. ICA algorithms are based on either second-order or higher-order statistics [54]. The ICA
algorithms based on higher-order statistics estimate W by maximizing statistical
independence of the probability density functions of individual sources using mutual
information or negentropy [7, 19]. The ICA algorithms based on second-order statistics estimate W by decorrelating the time-series data using the second-order blind
identification (SOBI) [20, 103]. ICA has been reported to perform well in EEG artifact removal due to its reasonable assumption of statistical independence between the
EEG signals and artifacts (e.g. see [2]). However, to explore statistical independence,
ICA needs the sufficient amount of EEG data [56]. Also, ICA works best when the
artifacts and the EEG signals remain stationary during the period of analysis, which
may not be the case in general. To ensure stationarity, studies have suggested an
epoch of 10 s or less, or a sample size in the order of multiples of
√
C where C
is the number of channels [56, 92]. When only a limited number of data samples
are available, studies have suggested using the ICA algorithms with second-order
statistics [28, 55].
Principal component analysis (PCA) has been proposed as a means to remove
artifacts from EEG [39, 67, 102]. PCA transforms presumably correlated multi-