  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.
