Eeg Inverse Problem: The State Space Theory

Estimating the information of electric activity source within the brain from the potential distribution measured on the scalp is called EEG (electroencephalographic) inverse problem. The research on EEG inverse problem is of great significance in both clinical application and neuroscience research. In order to increase the precision and reliability of the solutions, a new method based on state space model is proposed. The results indicate that this method is an effective way to solve the inverse problem. The main research work is based on giving an analysis on research status and scientific problems of EEG inverse problem:Due to theoretic difficulties of non-uniqueness problem, we should introduce suitable constraint conditions to the EEG inverse problem. The tradition methods usually give the constraint conditions from the perspectives of mathematics or physics. In this paper, we propose a method that based on state-space framework which under the electrophysiology constraint: the state equation is modeled by the electricity activity of cerebral neural network, and the measurement equation is modeled by the relationship between recorded potentials and source activity, these two equations constitute the state-space representation of EEG system. Then we use the kalman filter to solve this problem. The performance of the proposed method is evaluated using simulated phantom data and real EEG data with favorable results.Obtain the correct electrical conductivity of brain tissues is an important role in the research of EEG inverse problem, and a new method based on state space model is proposed: the conductivity is considered as a random variable of prior distribution, with the source localization, which are composed to state variable. Then, those variables are extended to a state equation with electrophysiology constraint. Similarly, the measurement equation is modeled by the relationship between recorded potentials and source activity. Finally, we adopt the dd1 method by which the electrical conductivity and the source localization can be achieved simultaneously. The results show that the method can estimate the electrical conductivity correctly, and we can use the conductivity information to improve localization precision at the same time. So the method is proved to be effective.