A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization

Abstract

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Fig.1

(a) The EEG source simulation here consisted of two gaussian-tapered patches, a superficial patch on the parietal gyrus and a deeper patch near the longitudinal fissure. Here color is scaled by dipole strength, red representing high strength and green low strength (blue=0). (b) The solution found using SBL and (c) by the proposed SCS algorithm (a) The simulated EEG source consisted of one gaussian-tapered patch. Solutions found using SBL (b,c) and SCS(d,e) with 10 and 5dB SNR

Fig.1

(a) The EEG source simulation here consisted of two gaussian-tapered patches, a superficial patch on the parietal gyrus and a deeper patch near the longitudinal fissure. Here color is scaled by dipole strength, red representing high strength and green low strength (blue=0). (b) The solution found using SBL and (c) by the proposed SCS algorithm (a) The simulated EEG source consisted of one gaussian-tapered patch. Solutions found using SBL (b,c) and SCS(d,e) with 10 and 5dB SNR

Fig.1

(a) The EEG source simulation here consisted of two gaussian-tapered patches, a superficial patch on the parietal gyrus and a deeper patch near the longitudinal fissure. Here color is scaled by dipole strength, red representing high strength and green low strength (blue=0). (b) The solution found using SBL and (c) by the proposed SCS algorithm (a) The simulated EEG source consisted of one gaussian-tapered patch. Solutions found using SBL (b,c) and SCS(d,e) with 10 and 5dB SNR

Fig.2

(a)–(c) SBL inverse solutions at steps 1, 15, and 30. (d)–(f) SCS inverse solutions at steps 1, 15, and 30. Here, color represents dipole strength, red representing high positive strength and blue, high negative strength (green=0).

Fig.3

(a) Mean disf at 30 iterations of SCS (black) and SBL (red) source inversion. (b) Mean normalized residual variance at each SCS (black) and SBL (red) iteration.

Fig.4

Mean distance between dipoles with highest strength in the SCS and SBL solutions at each iteration.