2 Preprocessing of EEG
23
2.3.2.3 Wavelet Transform and Empirical Mode Decomposition
EEG denoising can be achieved by decomposing a single-channel EEG signal into a
set of fundamental basis signals, with a premise that some basis signals may contain
the information of artifacts only. As such, we can find those artifact-related basis
signals and remove them from the decomposed set. Two representative methods for
decomposition of an EEG signal are presented below.
Wavelet transform convolves a given signal with a scaled and shifted version of
a mother wavelet function. It results in a set of coefficients corresponding to each
scale and time shift. The coefficients represent a similarity between a segment of the
signal and the mother wavelet at a given scale. The discrete wavelet transform (DWT)
is derived from continuous wavelet transform with discrete-time sampling. A basic
procedure of the DWT is filtering a signal with low- and high-pass filters, respectively,
where the low-pass filter works similar to the scaling function and the high-pass filter
works similar to the mother wavelet function [52]. Then, the low-pass filtered output
is passed to the next level of filtering with low- and high-pass filters again. This
procedure is repeated up to K levels and yields one approximation coefficient and K
detail coefficients where the approximation coefficient is obtained from the final lowpass filtering and the detail coefficients are obtained from a series of the high-pass
filtering through K levels. Then, for denoising, a threshold is applied to the detail
coefficients to sort out the ones with small magnitudes. It draws upon a hypothesis
that the signal can be strongly correlated with a properly chosen mother wavelet basis
at some levels whereas artifacts cannot be [104]. Finally, the artifact-reduced signal
is reconstructed by the refined detail coefficients and the approximation coefficient
[94]. Systematic ways of selecting a threshold can be found in some studies [34].
Empirical model decomposition (EMD) is a data-driven technique that decomposes a signal into a sum of the band-limited basis functions, called intrinsic mode
functions (IMFs) [49]. The IMFs have zero means and are amplitude and frequency
modulated. EMD has been shown to perform well with nonlinear and non-stationary
signals. If different sets of IMFs can separately represent the signal and artifacts,
we can reconstruct a clean EEG signal by removing artifact-related IMFs from the
decomposed set. EMD has been successfully applied to artifact removal of EEG
[70, 94, 115]. More advanced methods to overcome shortcomings of EMD (e.g. low
robustness against noise, no mathematical background), including ensemble EMD
(EEMD) [99, 116] and multivariate EMD (MEMD) [108], have also been adopted
for artifact removal.
2.3.2.4 Blind Source Separation
Blind source separation (BSS) has been most widely used for artifact removal when
the information about artifacts is limited—for instance, no reference is provided.
The basic BSS methods used for artifact removal assume a linear mixture model in
which the observed multi-channel EEG signals are assumed to be a linear mixture of
unknown sources with little knowledge about sources or a mixing matrix. The optimal
23
2.3.2.3 Wavelet Transform and Empirical Mode Decomposition
EEG denoising can be achieved by decomposing a single-channel EEG signal into a
set of fundamental basis signals, with a premise that some basis signals may contain
the information of artifacts only. As such, we can find those artifact-related basis
signals and remove them from the decomposed set. Two representative methods for
decomposition of an EEG signal are presented below.
Wavelet transform convolves a given signal with a scaled and shifted version of
a mother wavelet function. It results in a set of coefficients corresponding to each
scale and time shift. The coefficients represent a similarity between a segment of the
signal and the mother wavelet at a given scale. The discrete wavelet transform (DWT)
is derived from continuous wavelet transform with discrete-time sampling. A basic
procedure of the DWT is filtering a signal with low- and high-pass filters, respectively,
where the low-pass filter works similar to the scaling function and the high-pass filter
works similar to the mother wavelet function [52]. Then, the low-pass filtered output
is passed to the next level of filtering with low- and high-pass filters again. This
procedure is repeated up to K levels and yields one approximation coefficient and K
detail coefficients where the approximation coefficient is obtained from the final lowpass filtering and the detail coefficients are obtained from a series of the high-pass
filtering through K levels. Then, for denoising, a threshold is applied to the detail
coefficients to sort out the ones with small magnitudes. It draws upon a hypothesis
that the signal can be strongly correlated with a properly chosen mother wavelet basis
at some levels whereas artifacts cannot be [104]. Finally, the artifact-reduced signal
is reconstructed by the refined detail coefficients and the approximation coefficient
[94]. Systematic ways of selecting a threshold can be found in some studies [34].
Empirical model decomposition (EMD) is a data-driven technique that decomposes a signal into a sum of the band-limited basis functions, called intrinsic mode
functions (IMFs) [49]. The IMFs have zero means and are amplitude and frequency
modulated. EMD has been shown to perform well with nonlinear and non-stationary
signals. If different sets of IMFs can separately represent the signal and artifacts,
we can reconstruct a clean EEG signal by removing artifact-related IMFs from the
decomposed set. EMD has been successfully applied to artifact removal of EEG
[70, 94, 115]. More advanced methods to overcome shortcomings of EMD (e.g. low
robustness against noise, no mathematical background), including ensemble EMD
(EEMD) [99, 116] and multivariate EMD (MEMD) [108], have also been adopted
for artifact removal.
2.3.2.4 Blind Source Separation
Blind source separation (BSS) has been most widely used for artifact removal when
the information about artifacts is limited—for instance, no reference is provided.
The basic BSS methods used for artifact removal assume a linear mixture model in
which the observed multi-channel EEG signals are assumed to be a linear mixture of
unknown sources with little knowledge about sources or a mixing matrix. The optimal