Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practice of BSS based on second-order statistics (SOS) and on higher-order statistics (HOS), the latter better known as independent component analysis (ICA). Using neurophysiological knowledge we consider the fitness of SOS-based and HOS-based methods for the extraction of spontaneous and induced EEG and their separation from extra-cranial artifacts. We then illustrate a general BSS scheme operating in the time-frequency domain using SOS only. The scheme readily extends to further data expansions in order to capture experimental source of variations as well. A simple and efficient implementation based on the approximate joint diagonalization of Fourier cospectral matrices is described (AJDC). We conclude discussing useful aspects of BSS analysis of EEG, including its assumptions and limitations.

Abstract-This article describes a method to recover taskrelated brain sources in the context of multi-class BrainComputer Interfaces (BCIs) based on non-invasive electroencephalography (EEG). We extend the method Joint Approximate Diagonalization (JAD) for spatial filtering using a maximum likelihood framework. This generic formulation (1) bridges the gap between the Common Spatial Patterns (CSP) and Blind Source Separation (BSS) of non-stationary sources, and (2) leads to a neurophysiologically adapted version of JAD, accounting for the successive activations/deactivations of brain sources during motor imagery trials.Using dataset 2a of BCI Competition IV (2008) in which nine subjects were involved in a four-class two-session motorimagery (MI) based BCI experiment, a quantitative evaluation of our extension is provided by comparing its performance against JAD and CSP in the case of cross-validation as well as session-to-session transfer. Whereas JAD, as already proposed in other works, does not prove to be significantly better than classical one-versus-rest CSP, our extension is shown to perform significantly better than CSP for cross-validated and session-tosession performance. The extension of JAD introduced in this paper yields among the best session-to-session transfer results presented so far for this particular dataset, thus it appears of great interest for real-life BCIs.