Overcomplete Independent Component Analysis via Linearly Constrained Minimum Variance Spatial Filtering

Abstract. Independent Component Analysis (ICA) designed for complete bases is used in a variety of applications with great success, despite the often questionable assumption of having N sensors and M sources with NQM. In this article, we assume a source model with more sources than sensors (M>N), only L<N of which are assumed to have a non-Gaussian distribution. We argue that this is a realistic source model for a variety of applications, and prove that for ICA algorithms designed for complete bases (i.e., algorithms assuming N=M) based on mutual information the mixture coefficients of the L non-Gaussian sources can be reconstructed in spite of the overcomplete mixture model. Further, it is shown that the reconstructed temporal activity of non-Gaussian sources is arbitrarily mixed with Gaussian sources. To obtain estimates of the temporal activity of the non-Gaussian sources, we use the correctly reconstructed mixture coefficients in conjunction with linearly constrained minimum variance spatial filtering. This results in estimates of the non-Gaussian sources minimizing the variance of the interference of other sources. The approach is applied to the denoising of Event Related Fields recorded by MEG, and it is shown that it performs superiorly to ordinary ICA. Keywords: independent component analysis, blind source separation, overcomplete, underdetermined, EEG, MEG, denoising, event related fields, event related potentials, beamformin

Data-driven re-referencing of intracranial EEG based on independent component analysis (ICA)

Background: Intracranial recordings from patients implanted with depth electrodes are a valuable source of information in neuroscience. They allow for the unique opportunity to record brain activity with high spatial and temporal resolution. A common pre-processing choice in stereotactic EEG (S-EEG) is to re-reference the data with a bipolar montage. In this, each channel is subtracted from its neighbor, to reduce commonalities between channels and isolate activity that is spatially confined. New Method: We challenge the assumption that bipolar reference effectively performs this task. To extract local activity, the distribution of the signal source of interest, interfering distant signals, and noise need to be considered. Referencing schemes with fixed coefficients can decrease the signal to noise ratio (SNR) of the data, they can lead to mislocalization of activity and consequently to misinterpretation of results. We propose to use Independent Component Analysis (ICA), to derive filter coefficients that reflect the statistical dependencies of the data at hand. Results: We describe and demonstrate this on human S-EEG recordings. In a simulation with real data, we quantitatively show that ICA outperforms the bipolar referencing operation in sensitivity and importantly in specificity when revealing local time series from the superposition of neighboring channels. Comparison with Existing Method: We argue that ICA already performs the same task that bipolar referencing pursues, namely undoing the linear superposition of activity and will identify activity that is local. Conclusions: When investigating local sources in human S-EEG, ICA should be preferred over re-referencing the data with a bipolar montage