Journal ArticleEstimating the location and distribution of current sources within the brain from electroencephalographic (EEG) recordings is an ill-posed inverse problem. The ill-posedness of the problem is due to a lack of uniqueness in the solution; that is, different configurations of sources can generate identical external fields. Additionally, the existence of only a finite number of scalp measurements increases the under-determined nature of this problem. Most source localization algorithms attempt to solve the inverse problem by fitting the potenials created on the scalp from multiple dipoles to a single time step of EEG measurements. In this paper we consider a spatio-temporal model and exploit the assumption that the EEG signal is composed of contributions from statistically independent sources. Under this assumption, we can apply the recently derived blind source separation algorithm (BSS), also referred as to Independent Component Analysis (ICA). This algorithm separates multichannel EEG data into temporally independent activation maps due to stationary sources. For our study, we use a 64 channel EEG recording of a multi-focal epileptic event and a realistic geometric model of the cranial volume derived from MRI data. The original ICA algorithm required the number of sources to be equal to the number of recorded channels and becomes unstable otherwise. In this paper, we propose a novel approach for solving this problem through the reduction of the data subspace. Specifically, we discard eigenvectors with small eigenvalues from a PCA analysis of the data prior to ICA decomposition. Our results show that using these proposed subspace reduction methods, multi-focal epileptic data can be successfully decomposed into several independent activation maps. For each activation map we perform a separate source localization procedure, looking only for a single dipole using a multistart downhill simplex method. The localized sources are found to be located and oriented at physiologically appropriate positions within the brain
