4. Conclusions

could be overlapped. In addition, a presence of similar oscillations in different modes or a presence of disparate amplitude oscillations in the same mode, named "mode mixing" makes the performance of artifact rejection worse [60]. Signal distortion or attenuation typically occurs according to the above-mentioned methods by excessive interference. Thus, these

In linear regression, filtering, and ICA-based signal decomposition approaches, parameters W cannot often converge to a solution for perfectly demixing the mixtures. This implies that

Meanwhile, non-negative matrix factorization (NMF) [61] has recently attracted attention as effective algorithms to remove artifacts from single-channel signals because it can find the latent features underlying the interactions between EEG components and artifacts. An Mdimensional non-negative data vector x<sup>n</sup> is placed in the column of M · N matrix X, where N is number of data vectors. The matrix X is based on short-time Fourier transform and approximately factorized into an M · K nonnegative matrix H and a K · N nonnegative matrix W where K is the number of "basis" which is optimized for linear approximation of the input

partially restricting the active space should be determined for single-channel signals.

<sup>x</sup><sup>n</sup> <sup>≈</sup> <sup>y</sup><sup>n</sup> <sup>¼</sup> <sup>X</sup>

K

k¼1

where an h<sup>k</sup> and a wk,n denote an entry of H and W. This equation means that respective nonnegative EEG feature (power spectrum or amplitude spectrum) vector is approximated by linear combination of the basis vector h<sup>k</sup> weighted by the component of wk,n. Therefore, it can

Some works reported that the supervised NMF could effectively factorize the observed EEG signals into the brain activity components and the artifacts if the user has artifact data in advance [62, 63]. Before applying supervised learning, template matrix XArt has been factorized into HArt and WArt. The matrix X is continuously factorized into H and W where H contains the elements of matrix HArt. The matrix HArt has no relation to the elements of H while using standard NMF algorithm because the initial values are set randomly and updated by multiplicative rules. In supervised learning algorithm, the matrix HArt is used as a fixed value that will partially restrict the active space. By contrast, activity components in the matrix WArt are variable values. For this constraint, the matrix H can attempt to express EEG components in the matrix X with the

. EEG components will be stored in the bases (see Figure 8).

X N

HkWk,n

n¼1

After these processing, non-negative data of artifact-free EEG are reconstructed from the following

K

k¼KArtþ1

<sup>X</sup>^ <sup>¼</sup> <sup>X</sup> � <sup>X</sup>

hkwk,n, ð38Þ

X ≈ HW: ð39Þ

HW : <sup>ð</sup>40<sup>Þ</sup>

approaches are not suitable for real-time applications.

vectors. It can be represented by the following equation:

3.2.5. Nonnegative matrix factorization

82 Electroencephalography

be rewritten as

remaining based K<sup>0</sup>

equation:

By the properties of artifacts, theoretically multivariate statistical analysis approaches such as PCA and ICA, which separate multi-channel EEG signals into spatially and temporally distinguishable components, are useful for extracting EEG components from the scalp recordings. In particular, ICA is a powerful tool for separating observed EEG signals into maximally independent activity patterns derived from cerebral or non-cerebral (artifactual) sources. However, ICA is unsuitable for analyzing EEG signals recorded by specialized EEG device because of mismatching of its assumption in the single (or few) channel case. Thus, proposing a removal method of artifact from single-channel EEG signals is currently a major challenge in EEG signal processing for the widespread use of systems as a conventional technology.

In this chapter, we tried to summarize some existing artifact rejection algorithms (PCA, ICA, regression, filtering, ICA-based signal decomposition, and NMF) focusing on the advantages and disadvantages of algorithms, which would provide beneficial information to improve their performance in online EEG systems. Last but not least, muscular artifacts reflecting body actions are natural enemies of EEG systems. The inevitable encounter must be solved by artifact rejection techniques. During real-time EEG system operation using specialized devices, unsupervised learning algorithms cannot separate observed signal into EEG and EMG components so far. Neuroscientists and neuro-engineers should carefully analyze the characteristics of artifacts and integrate them in a supervised learning algorithm for effective rejection of artifacts or extraction of intrinsic EEG components from observed EEG signals without altering the underlying brain activity to routinely use EEG systems in the future.
