n this project, simulated EEG signals were separated using sparse signal representation.
Abstract
In this project, simulated EEG signals were separated using sparse signal representation. 3 different representations were compared as well as 3 different optimization methods.
Various conditions were tested by adding sensor noise as well as source noise.
The optimization method used was “”fast relative newton””.
It is shown that sparse representation for simulated EEG signals is significantly preferable for source separation. Further more, the “”fast relative newton”” method performs better than any other known optimization method regarding the source separation problem.
Introduction
EEG signals recorded at the scalp are assumed to be linear mixtures of (several) electric brain sources. Further more, each brain source is assumed to be composed of (few or many) electric dipoles, which independently exist at the skull.
Separating EEG signals into its brain sources has an enormous medical importance, hence the motivation for searching suitable algorithms for it.
While analyzing this problem, one can think of the ‘cocktail party’ problem in which stationary microphones record several guests talking simultaneously: Is it possible to separate each talking guest from the others?
The Problem
An array of sensors records a linear mixture of sources. Both sensors & sources
equal N. X denotes the data recorded at the sensors. S denotes the data generated by the sources. Both are N by T matrices.
The linear mixture is then given by the matrice M:
X=M·S.
Our aim: finding the matrices M,S given the measured matrice X.
The Solution
Using an optimization approach, one can develop the following objective function:
W is the unmixing matrice (M-1).
Tools
Using Matlab, six musical sources were mixed (after a relative attenuation of 8 dB), resulting in six sensors. Sensor noise and source noise were added. Source separation performance criterion was ISR (Interference Signal Ratio).
Main Results
Figure 1: sparse representation – time domain vs. spectrogram
Figure 2: ISR vs. source noise using spectrogram, derivative & time domain representation
(5th source only)
Figure 3: ISR vs. sensor noise using spectrogram, derivative & time domain representation
(5th source only)
Figure 4: ISR vs. CPU time – Comparing optimization methods
Conclusions
Adding relatively low source noise does not degrade the performance of source separation while using time domain, spectrogram nor derivative representations. This situation, though, changes with the increase of source noise level. Similar results were seen for all 6 sources examined.
Considering sensor noise, the spectrogram representation is preferable over all range of noise level. Similar results were seen for all 6 sources examined.
Regarding CPU time, the “”fast relative newton”” optimization method performs better than “”relative newton”” and InfoMax methods. These results were observed for all 6 sources regardless of the sparse representation used.
Acknowledgement
I would like to thank Michael Bronstein for his assistance and guidance.
I’m also grateful to the Ollendorff Minerva Center Fund for supporting this project.