Analysis on subtracting projection of extracted independent components from EEG recordings

Event-related potentials of electroencephalography (EEG) recordings can be assumed as mixtures of sources of electrical brain activities. To reject artifact sources, the projection of the estimated counterpart by independent component analysis (ICA) is often subtracted from EEG recordings. However, the association of performance of ICA decomposition and the subtraction has never been analyzed before. Coincidently, we find that a source can be completely removed from EEG recordings through the subtraction theoretically. The necessary condition of such results is that the estimated ICA model for every source should be entirely correct, that is, each estimated source is just the scaled version of one source. Meanwhile, we also find that the subtraction cannot sufficiently reject one source practically. This is because the estimated ICA model for some sources is inevitably incorrect, that is, some estimated sources are still the mixture of a few sources. To improve the accuracy of the subtraction, it is first necessary to develop better ICA algorithms to separate mixtures as sufficiently as possible and secondly it is necessary to modify the abnormal polarity of the projection of the estimated source in the electrode field. Numerical simulations validate the effectiveness of the modification on the abnormal polarity in rejecting one source.