What Are the Best Tips for EEG Analysis?

The EEG signal analysis method ^[1] has developed rapidly in recent years and has begun to be applied to the clinic, further improving the diagnostic effect.

Chinese name: EEG signal analysis

Foreign name: EEG analysis
profession: Signal analysis method

Background of EEG signal analysis

Electroencephalogram (EEG) is the overall reflection of the electrophysiological activities of brain nerve cells on the cerebral cortex or scalp surface. EEG signals contain a large amount of physiological and disease information. In clinical medicine, EEG signal processing can not only provide a basis for diagnosis of certain brain diseases, but also provide an effective treatment for certain brain diseases. In engineering applications, people have also tried to use brain electrical signals to implement the brain-computer interface (BCI), to take advantage of the differences in the human brain's EEG signals for different sensory, motor or cognitive activities. To achieve some control purpose ^[2] . However, since the EEG signal is a non-stationary random signal with no ergodic states ^[3] , and its background noise is also very strong, the analysis and processing of the EEG signal has always been a very attractive but difficult study. Topic.

Since Dietch first performed the EEG analysis with the Fourier transform in 1932, classical methods such as frequency domain analysis and time domain analysis have been successively introduced in EEG analysis. In recent years, wavelet analysis, matching tracking method, neural network analysis, chaos analysis and other organic methods have been applied in EEG analysis ^[4] , which has strongly promoted the development of EEG signal analysis methods.

EEG signal analysis method

EEG signal analysis in frequency domain

Power spectrum estimation

Power spectrum analysis is the most commonly used tool for EEG signal processing. It is derived from Fourier transform. Its premise is a stationary random signal. For unbalanced random signals, the spectral analysis results at different times are different. One of the commonly used methods is the periodic method based on the Fourier transform of short-term cut data. The specific method is to segment the actual Huai signal in the time domain and consider it to be quasi-stationary. The resulting squared amplitude-frequency characteristic is then multiplied by an appropriate window function to estimate the power spectrum of the signal. However, this method has poor frequency resolution, side-lobe leakage, and large spectral estimation variance.

EEG signals (EEG) are non-stationary random signals ^[3] . Its correct expression and accuracy of frequency domain characteristics, extraction of phase information, and transient waveform analysis are hot topics in current EEG signal processing research. However, due to the common problems of spectral analysis methods, the variance characteristics of the estimates are not good, and the fluctuations of the estimates along the frequency axis are more severe. The longer the data, the more serious this phenomenon is. Therefore, a parameter model spectral estimation method is proposed. This method can obtain high-resolution spectral analysis results for data processing, thereby providing a new and effective method for extracting the frequency domain features of EEG signals, especially in dynamic characteristics analysis.

AR parameter model spectrum estimation

AR model of EEG signals:

X _k is the actual value of the EEG signal: _i is the model parameter: m is the model order; Wk is the zero-mean stationary Gaussian noise. The AR model coefficients are easier to obtain from solving linear equations or recursive calculations than MA and ARM A. The random signal studied in the model is the output of a stationary white noise excited linear filter. The AR model first selects the best order problem.The commonly used ordering criteria are information theory criterion (AIC), final prediction error criterion (FPE), etc., after the order is determined, the mean square error between the signal data column and its estimator is the smallest. Criterion, find the value of ak. The algorithms of AR coefficients ^[5] include Yule-Walker, Burg algorithm, Least Squares, etc., each with advantages and disadvantages.

Bispectrum analysis

Power spectrum analysis can effectively reflect the second-order information of the signal, but the higher-order information including phase information is lost, and this information is sometimes very meaningful for EEG signal analysis. The bispectral density function is defined as:

C _x is the third-order center moment of the stationary random process x (t). m _x is the mean of x (t). The bispectral function only contains the phase information of the signal, but does not give the phase information. For the Gaussian random distribution, the bispectrum is a measure of the deviation of the random signal from the Gaussian distribution. Examination of the actual EEG data shows that the deviation of the EEG from the Gaussian distribution in different functional states is quite different. Such as the use of AR models for bispectral analysis. The third-order recursive (TOR) method is used to estimate the bispectrum and analyze the characteristics of EEG in focal ischemic brain injury.It can be seen that the distribution of EEG bispectrum in the injured area changes. At different stages of the injury, the injured area and the non-injured area The bispectral maxima and the weighted bispectral center (WCOB) have significantly different changes ^[6] .

Bispectrum analysis requires the signal to be at least third-order stationary, so it is meaningful for short data EEG signals.

EEG signal analysis time domain analysis

Extracting features directly from the time domain ^[7] is the earliest developed method, because it is intuitive and has a clear physical meaning, so many EEG doctors or technicians still use it. In the past, EEG analysis mainly relied on the naked eye, which can be regarded as artificial time domain analysis. Time domain analysis is mainly used to directly extract waveform features, such as zero-crossing intercept analysis, histogram analysis, variance analysis, correlation analysis, peak detection and waveform parameter analysis, coherent averaging, waveform identification, and so on.

Time-frequency analysis of EEG signals is a time-varying, non-stationary signal with different frequency components at different times.The simple time-frequency analysis method is related by Fourier transform.They are completely separated by the frequency of the signal. It is premised that the invariant characteristic or the statistical characteristic is stable. However, due to the uncertainty principle of time and frequency domain resolution, it is impossible to obtain higher resolutions in both time and frequency domains. Moreover, many lesions in the EEG are presented in a transient form. Only by combining time and frequency for processing can better results be obtained. It can be said that the time-frequency representation of signals provides very good prospects for EEG signal processing. At present, the more widely used methods are Wigner-VilleDistribution (WD) and wavelet transform. The matching tracking method has also been used in the analysis of sleep ^[8] spindle waves.

EEG signal analysis wavelet transform

The wavelet transform has (1) multi-resolution (multi-scale); (2) the figure of merit, that is, the relative bandwidth (the ratio of the center frequency to the bandwidth) is constant; (3) the proper selection of the basic wavelet can make the wavelet ^[9] in Both the time and frequency domains have the ability to characterize the local characteristics of the signal. When a smaller scale is used, the observation range on the time axis is small, and in the frequency domain, it is equivalent to use a higher frequency for higher resolution analysis, that is, to use HF wavelets for detailed observation. The observation range on the axis is large, while in the frequency domain, it is equivalent to using low-frequency wavelet for overview observation. Therefore wavelet transform is known as "mathematical microscope".

(ANN) EEG signal analysis artificial neural network (ANN) analysis

A neural network is a network that is widely interconnected by a large number of processing units. It reflects the basic characteristics of human brain function, and it is a kind of abstraction, simplification and simulation of human brain. The information processing of the network is realized by the interaction between neurons; the storage of knowledge and information manifests as a distributed physical connection between the interconnection of network elements; the learning and identification of the network depends on the dynamic evolution of the connection weight coefficients of each neuron . The neural network can be used for spontaneous electroencephalogram (EEG) analysis. The purpose of the analysis is to detect EEG spikes and seizures. The input method can use the original signal model and characteristic parameter model. There are currently methods that use a combination of wavelet transform and artificial neural network to detect spike and spike components in EEG signals ^[10] . The wavelet transform ^[11] (WT) was used to preprocess the input of the EEG spike detection system based on ANN, so as to reduce the input scale of ANN without reducing the information content of the signal and the detection performance.

EEG signal analysis nonlinear dynamic analysis

In recent years, with the development of non-linear dynamics, more and more evidence shows that the brain is a non-linear dynamic system, and EEG signals can be regarded as its output. Therefore, people try to use some methods of nonlinear dynamics, such as fractal dimension, Lorenz scatter plot, Lyapunov exponent, complexity, etc., to analyze EEG signals in order to gain a new understanding of the brain ^[12] . The Lorenz scatter plot of the EEG signal refers to a graph obtained by plotting the first point of two adjacent sampling points of the EEG signal as the abscissa and the next point as the ordinate. The data show that the values of adjacent sampling points of the EEG signal of epilepsy patients are close and the distribution range of the value of the entire EEG signal is large, while the points in the Lorenz scatter diagram of normal EEG signals are mostly distributed in a range. Small oval area.

Preliminary research shows that the electroencephalogram dynamics characteristics show great scientific and application value ^[13] . It provides information that cannot be obtained by conventional analysis methods based on physical ideas, and is not affected by special points and repeatable. The advantages.

EEG signal analysis

EEG signals are obvious non-stationary signals. Since the detection of EEG signals in the 1920s ^[14] , although a lot of work has been done, no breakthrough has been made for a long time. With the continuous development of signal processing methods ^[3] , more and more effective analysis methods are applied to the analysis of EEG signals. People will have a further understanding of the mechanism of EEG activity ^[15] , and it will also be a new technology for clinical The development of basic medicine has made new contributions.