EEG extended source localization: tensor-based vs. conventional methods.

The localization of brain sources based on EEG measurements is a topic that has attracted a lot of attention in the last decades and many different source localization algorithms have been proposed. However, their performance is limited in the case of several simultaneously active brain regions and low signal-to-noise ratios. To overcome these problems, tensor-based preprocessing can be applied, which consists in constructing a space-time-frequency (STF) or space-time-wave-vector (STWV) tensor and decomposing it using the Canonical Polyadic (CP) decomposition. In this paper, we present a new algorithm for the accurate localization of extended sources based on the results of the tensor decomposition. Furthermore, we conduct a detailed study of the tensor-based preprocessing methods, including an analysis of their theoretical foundation, their computational complexity, and their performance for realistic simulated data in comparison to conventional source localization algorithms such as sLORETA, cortical LORETA (cLORETA), and 4-ExSo-MUSIC. Our objective consists, on the one hand, in demonstrating the gain in performance that can be achieved by tensor-based preprocessing, and, on the other hand, in pointing out the limits and drawbacks of this method. Finally, we validate the STF and STWV techniques on real measurements to demonstrate their usefulness for practical applications.