Reliable independent component estimation using expectation maximized iterative subset decomposition of noise-perturbed multichannel EEG/MEG recordings

A major problem in electro-/magnetoencephalography (EEG/MEG) is obtaining reliable information about the underlying signals of neural sources. This problem arises on the one hand from the volume conducting property of the head. Electric potentials/magnetic fields generated by the currents of an unknown huge number of neural sources are instantaneously and consistently present in all EEG/MEG sensors. Consequently each sensor signal consists of a distinct weighted linear superposition of all source signals, resulting in an underdetermined unknown mixing system. On the other hand subsequent perturbation in terms of sparsely mixed sensor noise is inevitably added by the recording equipment. Thus, hardly any conclusions about the source signals can be drawn without previous knowledge or assumptions about the sources and the mixings. In the past ICA (independent component analysis) has been applied to EEG/MEG data, to estimate neural source signals via decomposition of sensor signals into statistically independent components (ICs). However, a known issue in ICA is the reliable estimation of source signals in case of noise-perturbation and the restricted applicability to non-square decomposition in case of over-/underdeterminacy. We propose two novel ICA methods to estimate neural source signals, embedded in noise-perturbed underdetermined mixing systems. According to the basic ICA model, the proposed methods take advantage of the non-sparse mixing of neural source signals to estimate the most reliable ICs being present in all sensor signals. Both methods involve iterative decomposition of different data subsets and optimal IC clustering via an extended Hungarian algorithm. Additionally successive expectation maximization and global mixing matrix reconstruction is used to constrain the data / parameter space and to attenuate noise. We applied the methods to multichannel EEG/MEG but also to simulated intracortical single-channel multi-trial data and validated the performance using toydata with densely mixed ICs embedded in sparsely mixed noise. Our results show that in contrast to other ICA methods no dimension reduction is necessary to perform a noise-reduction, while the resulting information conservation and the exploit of the multivariate data statistics additionally increase the estimation reliability. Furthermore the results suggest that a revealing of neural source signals and a reconstruction of the global non-square mixing matrix are possible, if the number of sources is less than the available sensors. The methods were implemented in MATLAB® and are available as an EEGLAB plug-in or as a standalone toolbox from the author's webpage