eeg analysis during hypnagogium petr svoboda laboratory of system reliability faculty of...
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![Page 1: EEG analysis during hypnagogium Petr Svoboda Laboratory of System Reliability Faculty of Transportation Czech Technical University e-mail: svobodap@spel.cz](https://reader035.vdocuments.mx/reader035/viewer/2022062321/56649f315503460f94c4ce33/html5/thumbnails/1.jpg)
EEG analysis during hypnagogium
Petr SvobodaLaboratory of System ReliabilityFaculty of TransportationCzech Technical University
e-mail: [email protected]
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Presented methods
Traditional methodsFourier transform
Parametrical methodsAutoregressive estimator
Nonlinear methods - Chaos theoryDelay-time embedding, Correlation dimension, Takens estimator, State Space dimension, Lyapunov exponents
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EEG activity
Name Freq. [Hz]
Deltha 0,5-4Theta 4-8Alpha 8-15Beta 15-35
electric potential of brain‘s neural activity registered on the skelet four basic frequencies
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Traditional methods
Signal‘s stationarity frequency resolution leakage of frequency spectraquality of the spectral estimatephase of the signal is lost
Potencial problems
Estimate of a periodogram using the Fourier transform
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Parametric model
Autoregressive (AR) model:
Approximation of an EEG signal by adequate parametric model
Approximation of an EEG signal by linear time invariant filter with transfer function H(z)=1/A(z)
Whitening of signal by AR filter:
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Analyzed signal
Pole placement
Autocovariance function
Spectral estimate
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Comparison of traditional and parametric methods
Parametric methods:
+ frequency resolution+ parametric description of analyzed signal - estimate of AR model order - high noise sensitivity
Traditional methods:
+ low noise sensitivity - frequency resolution
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Microsleep classification
+ Alpha, deltha and theta activity of spectral estimate
Traditional methods
Parametrical methods+ Alpha, deltha and theta activity of spectral estimate- estimate of AR model order- placement of poles in a complex plane
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Classification by spectral estimate
Classification into 2 states•RELAXATION•DROWSINESS
Classification based on neural network (back propagation)
Classical methods: accuracy of about 87%
Parametrical methods: accuracy of about 90%
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Relaxation
Drowsiness
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Chaos theory
analysis of dynamic deterministic systems• high sensitivity on initial conditions• known dynamics and phase of the system
detecting nonlinearity by surrogate data testing
delay-time embedding• state-space dimension estimate• estimate of delay time
estimate of fractal dimension D2
Takens estimator for D2 dimension largest Lyapunov exponents
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Delay-time embedding
Si=[x(i),x(i+L),… x(i+(m-1)L)]
L… time delaySi… state-space vectorm… state dimensionx… analyzed signal
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Selection of Delay Time L
Time delay should be set so, x(i),x(i+L),… are independent
autocorrelation methodmethod of Mutual Information (MI)
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Fractal dimension & Takens estimator
Fractal dimension is a measure of complexity of the analyzed signal
D2 = log C(r) / log r
Where C(r) is correlation integral
D2 computed by maximum likelihood estimator is known as Takens estimator
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Microsleep classification
+ matematical description of state-space trajectory reconstructionnonlinearity detection
- correlation dimension D2 estimate
+ Takens estimator+ largest Lyapunov exponents
Chaos theory
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Largest Lyapunov Exponents
Sensitive dependence on initial conditions