EEG Signal Processing and Machine Learning. Saeid Sanei

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Название EEG Signal Processing and Machine Learning
Автор произведения Saeid Sanei
Жанр Программы
Серия
Издательство Программы
Год выпуска 0
isbn 9781119386933



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(m − 1)th frame are then used to predict the first sample in the mth frame, which we denote it as images. If this error is small, it is likely that the statistics of the mth frame are similar to those of the (m − 1)th frame. Conversely, a large value is likely to indicate a change. An indicator for the fourth criterion can then be the differentiation of this signal (difference of digital signal) with respect to time, which gives a peak at the segment boundary, i.e.:

      Finally, a fifth criterion d 5(m) may be defined by using the AR‐based spectrum of the signals in the same way as short‐time Fourier transform (STFT) for d 3(m). The above AR model is a univariate model, i.e. it models a single‐channel EEG. A similar criterion may be defined when multichannel EEGs are considered [14]. In such cases a multivariate AR (MVAR) model is analyzed. The MVAR can also be used for characterization and quantification of the signal propagation within the brain and is discussed in Chapter 8 of this book.

      Although the above criteria can be effectively used for segmentation of EEG signals, better systems may be defined for the detection of certain abnormalities. In order to do that, the features, which best describe the behaviour of the signals, need to be identified and used. Therefore, the segmentation problem becomes a classification problem for which different classifiers can be used.

Schematic illustration of (a) An EEG seizure signal including preictal, ictal, and postictal segments, (b) the error signal and (c) the approximate gradient of the signal, which exhibits a peak at the boundary between the segments.

      Parametric spectrum estimation methods such as those based on AR or autoregressive moving average (ARMA) modelling can outperform the DFT in accurately representing the frequency‐domain characteristics of a signal, but they may suffer from poor estimation of the model parameters mainly due to the limited length of the measured signals. For example, in order to model the EEGs using an AR model, accurate values for the prediction order and coefficients are necessary. A high prediction order may result in splitting the true peaks in the frequency spectrum and low prediction order results in combining peaks in close proximity in the frequency domain.

      (4.16)equation

      where, E(ω) = Kω (Constant), is the power spectrum of the white noise and Xp (ω) is used to denote the signal power spectrum. Hence,

      (4.17)equation

      The fluctuations in the signal DFT as shown in Figure 4.3b is a consequence of the statistical inconsistency of periodogram‐like power spectral estimation techniques. The result from the AR technique (Figure 4.3c) overcomes this problem provided the model fits the actual data by selecting a proper prediction order for the AR estimates. EEG signals are often statistically nonstationary, particularly where there is an abnormal event captured within the signals. In these cases the frequency‐domain components are integrated over the observation interval and do not show the characteristics of the signals accurately. A TF approach is the solution to the problem.

      In the case of multichannel EEGs, where the geometrical positions of the electrodes reflect the spatial dimension, space–time–frequency (STF) analysis through multiway processing methods has also become popular [15]. The main concepts in this area together with the parallel factor analysis (PARAFAC) algorithm will be reviewed in Chapter 17 aimed at detection of movement‐related potentials or eye‐blinking artefacts from the EEG signals.

      The STFT is defined as the discrete‐time Fourier transform evaluated over a sliding window. The STFT can be performed as:

      (4.18)equation

      (4.19)equation

      Based on the uncertainty principle, i.e. images, where images and images are respectively time and frequency‐domain variances, perfect resolution cannot be achieved in