A New Approach for Brain Source Position Estimation Based on the Eigenvalues of the EEG Sensors Spatial Covariance Matrix Lucas F. Cruz, Marcela G. Magalhães, Jonas A. Kunzler, André A. S. Coelho, and Rodrigo P. Lemos Abstract Direction of Arrival (DOA) estimation methods, like MUSIC, can be applied to EEG signals for brain source localization. However, they show a severe degradation at small signal-to-noise ratios on the EEG sensors and for large amounts of brain sources. Inspired on the SEAD method, this article introduces a new method that analyses the eigenvalues of a modified spatial covariance matrix of the EEG signals to produce a two-dimensional spectrum whose peaks more robustly estimate the source positions on a horizontal section of the brain. The key approach is to select the eigenvalues that are less affected by the noise and use them to produce the spectrum. To assess the accuracy and robustness of the proposed method, we compared its root-mean-square-error performance at dif- ferent noise conditions to those of MUSIC and NSF. The proposed method showed the lowest estimation errors for different amounts of brain sources and grid densities. Keywords Biomedical engineering  DOA  Eigenvalues Source estimation 1 Introduction The human body produces several biopotentials related to its electrochemical activities, which are an important source of information. Electroencephalography (EEG) was born by the hands of Hans Berger and it is characterized by measure- ments of those biopotentials on the scalp [1]. For its non- invasive nature, EEG still is a fairly current tool to diagnose several brain disorders, including epilepsy syndromes. Nearly 1–2% of world population are affected by epilepsy disorder, which is divided in two categories: partial and generalized epilepsy. Partial epilepsy is defined as a seizure that is originated only on a neuron group and shows high drug resistance. There is a surgical indication for those cases, however such indications and the surgical technique to be employed are both related to the location and number of epileptogenic foci (EFs) [2]. Therefore, estimation methods are useful to identify the sources positions which in turn allow classifying signals regarding their frequencies and determining the EFs after the use of beamforming algorithms. Source position estimation can be accomplished with DOA (Direction of Arrival) techniques. The MUSIC (MUltiple SIgnal Classification) algorithm, a widespread method due to its easy implementation, can be used to brain source estimation [3]. Based on orthogonal subspaces, this algorithm makes a sweep in a search grid, where the orthogonality between a simulated signal subspace and an estimated noise subspace generates peaks in the source positions. Another largely used DOA method is the NSF (Noise Subspace Fitting) [4], such that we decided to apply it for the first time to the brain source position estimation in this paper due to its versatility. The NSF explores the subespace fitting between an estimated noise subspace and a simulated signal subspace through the inverse of Frobenius norm. A sweep of the simulated signal creates peaks in the source positions, where the Frobenius norm attains its minimum. Under low L. F. Cruz (&)  M. G. Magalhães  J. A. Kunzler A. A. S. Coelho  R. P. Lemos School of Electrical, Mechanics and Computer Engineering, Universidade Federal de Goiás - UFG, Goiânia, Goiás, Brazil e-mail: fiorini.cruz@gmail.com M. G. Magalhães e-mail: mar.cela.gm@hotmail.com J. A. Kunzler e-mail: k.jonasaugusto@gmail.com A. A. S. Coelho e-mail: andreproj1@gmail.com R. P. Lemos e-mail: V.lemos@ufg.br © Springer Nature Singapore Pte Ltd. 2019 L. Lhotska et al. (eds.), World Congress on Medical Physics and Biomedical Engineering 2018, IFMBE Proceedings 68/2, https://doi.org/10.1007/978-981-10-9038-7_50 271