Complex Spectral-domain Independent Component Analysis of Electroencephalographic Data

Independent component analysis (ICA) has proved to be a highly useful tool for modeling brain data and in particular electroencephalographic (EEG) data. In this paper, a new method is presented that may better capture the underlying source dynamics than ICA algorithms hereto employed for brain signal analysis. We suppose that a brief, impulse-like activation of an effective signal source elicits a short sequence of spatio-temporal activations in the measured signals. This leads to a model of convolutive signal superposition, in contrast to the instantaneous mixing model commonly assumed for independent component analysis of brain signals. In the spectral-domain, convolutive mixing is equivalent to multiplicative mixing of complex signal sources within distinct spectral bands. We decompose the recorded mixture of complex signals into independent components by a complex version of the infomax ICA algorithm. Some results from a visual spatial selective attention experiment illustrate the differences between real time-domain ICA and complex spectral-domain ICA, and highlight properties of the obtained complex independent components.