Study On The Numerical Solutions For Localizing The Sources Of Electroencephalogram

In this paper, the methods for solving the EEG inverse problem are investigated in details and the research work is focused on the following several aspects: (1) Some problems in the HEM numerical solution process based on realistic head model and related techniques are analyzed. The isolated problem with an adjustable parameter is introduced to solve the ill-conditioning problem caused by the low conductivity value of the skull. A new thought and a corresponding application software are developed. (2) A novel method of applying wavelet neural network to the study of source localization based on equivalent current dipole is presented. The difficulty in the description of inverse model and the disadvantage of the high computational cost of iterative approaches are avoided. A self-memory is established in the training of wavelet network, which can determine the inner relation between the observation EECI on the scalp and the electric current sources in the brain correctly. The parameters of the sources can be worked out rapidly for new EEG data, providing a new approach to the dynamic analysis of EEG. (3) Based on the single-scaling wavelet frame theory and radial basis function neural network, a multi-dimensional input and output wavelet network is constructed. In order to handle problems of high dimension EEG inverse problem, we develop the algorithms whose implementations are less sensitive to the dimension. The main idea includes: (a) selection of suitable wavelet functions within regular wavelet lattice according to the information of input samples, and (b) an adaptive orthogonal projective algorithm which can determine the size and the connecting weights of the network in the light of the information given by output data. (4) As to the distributed source representation, a hybrid weighted minimum norm solution is presented. Based the physiological result that the sources exhibit the high level of coordination and the sparse focal characteristics, the weighted matrices are constructed stage by stage to give constraints to the inverse solution gradually. In simulation studies, more acceptable results can be obtained by the hybrid weighted minimum norm approach.