The project goal is finding an algorithm which will improve existing techniques used to filter evoked potentials (EP) from electrical brain signals (EEG).
Abstract
The project goal is finding an algorithm which will improve existing techniques used to filter evoked potentials (EP) from electrical brain signals (EEG).
EP’s are the brain reaction to different external stimulus.
Our algorithm can be used to improve existing methods and filter the EP with greater accuracy.
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The Problem
The EEG signal is registration of electrical activity in the brain. The activity us registered by placing electrodes on the scalp and measuring the voltage on them. The electrical activity is do firing great number of neurons in the brain. Temple firing always appears in the measures, but different patterns appear as a result of awakening state and other parameters .The parts of the EEG that comes from external evoking belongs to the part of the brain activity that is called evoked potential EP Different amplitudes and frequencies characterize slow potentials that are usually interest. Another characterize is that they have a very low signal to noise ratio SNR. This makes it very hard to identify them from signal measurements.
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Solution
Our solution based on Discrete Wavelet Transform (DWT) and well known Statistical Method ‘Maximum Likelihood’. The solution applied to wide range of problems were required denoising of weak signals on the noise background. The used method will denoise the weak signals with spectrum overlapped with noise unlike usual frequency filtering. The algorithm uses a prior information to approximate a form of the brain signals. This information used to generate like to EP signals which help us to construct dictionary of appropriate wavelets. The projection of noisy signal on the base functions from this dictionary result in loosing of noise energy. The full algorithm of estimating clean (EP signal) signal may be shown as follow:
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The core of the method is a Statistical Facet Model :
n – noise
W – matrix of Orthogonal wavelets (small number of column)
c- vector of coefficients
s- noisy signal
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The statistical method suggests solution for denoising in the following form:
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covariance matrix of noise
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The results strongly depend on the nature of signal and noise. The reconstruction of the signal from noisy one was obtained on range of 5db .. -20db.
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Acknowledgements
We would like to thank our supervisor, Pavel Kisilev , for his patience and for guiding us through the project and the Ollendorff Minerva Center fund for their support.
We would also like to thank Johanan Erez and the rest of the laboratory staff for their help and support.