Linear spatial filters (e.g., ICA, PCA) cannot perfectly extract EEG/MEG sources

Linear spatial filters (LSFs) derived from techniques like independent component analysis (ICA) or principal components analysis (PCA) are extremely popular techniques for analyzing electroencephalographic (EEG) and magnetoencephalographic data. They work by exploiting the fact that different EEG/MEG signal sources (e.g., a cortical patch or the eyes) project across the scalp with different topographies. An LSF can ignore signals by being orthogonal to their topographies, which makes them useful tool for isolating strong EEG/MEG sources (e.g., blinks, alpha/mu generators).

An under-appreciated limitation of LSFs though is that they cannot perfectly isolate a single EEG/MEG source. This stems from the fact that there are thousands of EEG/MEG sources and, at best, hundreds of EEG/MEG sensors (Groppe et al., 2008). Consequently, it is surely impossible for an LSF to be orthogonal to all EEG/MEG sources save for the one of interest (see proof below).  That being said, if an EEG/MEG source is strong (e.g., a blink potential), ICA can still be highly effective at isolating it, albeit with negligible contamination from other sources.

Groppe, D. M., Makeig, S., & Kutas, M. (2008). Independent component analysis of event-related potentials. Cognitive Science Online, 6(1), 1-44.

lsf_proof

 

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