Extension of the visibility concept for EEG signal processing

Objective. Visibility is an intrinsic property of any network of sensors that describes the regions in which its measurement sensitivity is concentrated. Initially introduced to describe the global spatial sensitivity of air pollution monitoring networks, we propose to extend the concept of visibility to characterize the detection capabilities of electroencephalography (EEG) systems utilized to measure brain electrical activity.Approach. In this paper, we represent visibility within the brain as a field of symmetric 3 × 3 matrices, satisfying the so-called 'renormalization conditions' and interpreted as second-order tensors. A compact and computationally efficient iterative algorithm is proposed for computing this tensor field. In addition, we explain how to visualize and present the visibility information in an intuitive and easily understandable way.Main results. The visibility concept is exploited to evaluate and compare the ability of three consumer-grade EEG headsets to detect and localize an arbitrary current distribution in the brain. Additionally, visibility is applied to derive an inverse solution that can solve the neuroelectromagnetic inverse problem (NIP) by reconstructing focal brain sources from EEG data.Significance. Although the lead field function approach can be employed to describe the sensitivity of individual electrodes from an EEG headset, this paper extends the sensor network's visibility concept to characterize the sensing capabilities of a complete EEG system. The comparison between three consumer-grade EEG headsets shows that the size of the low-visibility brain area decreases when the number of electrodes used increases. In addition, we show that the source parameters are best estimated by the inverse solution when they are oriented towards the maximum visibility direction.