Research On EEG Source Localization Based On Nonlinear Optimization Methods And Independent Component Analysis

Estimating the electric current sources within the brain from electroencephalographic (EEG) recordings is called the inverse problem of EEGThe source localization of equivalent current dipoles is an important issue on EEG inverse problem. The simplified asymmetrical concentric three-sphere model and the classical inhomogeneous concentric three-sphere volume conductor model were adopted in this thesis. Based on instantaneous-state dipole model (ISM) and spatio-temporal source model (STSM), simulation studies were made on EEG dipole source localization by using newly developed nonlinear optimization methods and independent component analysis algorithms.Based on the simplified asymmetrical concentric three-sphere model and ISM, nonlinear local optimization methods, such as Simplex and Levenberg-Marquart algorithms, were used to solve EEG dipole source localization problems. The relationship between location errors and noise level was discussed on the condition that the source number was known. If the source number was not known, the selected number in model may not equal to the actual one. To overcome this, a computation was carried out and a corresponding discrimination criterion was proposed. We also introduced genetic algorithm (GA) to EEG source localization and compared its performances with that of Simplex and LM algorithms.Based on classical inhomogeneous concentric three-sphere volume conductor model and STSM, a hybrid generic algorithm (HGA) which combined generic algorithm with local search algorithm was also introduced for EEG dipole source localization and was compared with nonlinear local optimization methods. Satisfactory localization results were achieved. Also, the noise level that could be accepted by reasonable source localization results by using HGA was analyzed.Also based on classical inhomogeneous concentric three-sphere volume conductor model and STSM, a Quasi-Newton algorithm based on ICA (Quasi-Newton-ICA) was applied for EEG multiple dipole source localization. Its performance was evaluated under high noisy environment for two dipole sources and three dipole sources by computer simulations. Because this method localized each dipole separately, the results were as stable as those for the single dipole, but the search complexity was dramatically reduced. Simulations were also carried out to examine the feasibility of improving multiple dipole localization result when substantial measurement noise exists by applying Quasi-Newton-ICA approach on different sample points.When the assumption of source independence is satisfied, applying ICA to the simulated EEG data would still introduce one problem that is to ensure appropriate ratios between the number of electrodes and the number of time points in the data used for analysis. In our simulation, we found that the sampling frequency was an important factor which affected the ratio and we compared the appropriate ratios for different sampling frequencies.For real EEG experiments, there are a lot of spatially correlated noises and the real noise with the spatially correlated colored noises should be used. In this thesis, we designed a spatial filter with linearly constrained minimum variance. The GWN matrix which was white on both space and time was used for the filter, and thus the spatially correlated noise (SCN) was obtained. The localization results with SCN were compared with that of Gauss white noise.The present study demonstrates the substantially enhanced performance of ICA-based multiple-source localization method for low SNR data, and its applications to independent multiple neural sources would play an important role in advancing the source localization and neuroscience research.