Effects of source space resolution, randomization and averaging in focal EEG source localization: Estimation of forward and inverse errors

Abstract

In this article, we study randomized multiresolution forward modeling and source localization in electroencephalography (EEG). Our goal is to determine numerically the effects of variable source space resolution on both forward modeling and source localization perspectives and to examine how it affects the detection of the sources at different depths inside the brain. Our concentration is in the main principles of multiresolution methods: random source space generation and the reconstruction obtained via averaging over multiple maximum a posteriori (MAP) estimations obtained at a finite set of different sub source spaces, and their suggested enhancement in distinguishability of weak components. The motivation of averaging is to reduce the discretization and optimization error and marginalize other variable factors. Due to the unguided randomized source space generation, multiple samples of the same size source spaces are needed. For this very reason, a large number of source spaces of multiple source counts are used to obtain statistically feasible results in this paper. This study verifies the described postulates of the multiresolution technique by showing averaging to be crucial in order to obtain a robust projection to a lower resolution, where the lead field matrix is overdetermined. From the viewpoint of source localization, the multiresolution approach was found to improve the reconstruction accuracy obtained with each resolution level below the highest and observed to be necessary to achieve an accuracy comparable to that of forward modeling.