Fundamental limits on source-localization accuracy of EEG-based neural sensing

In this paper, we obtain information-theoretic fundamental limits on attainable source-localization accuracy in Electroencephalography (EEG) recordings of the brain. To develop a systematic approach, we borrow idealized models of the human head from neuroscience literature and analyze the brain-activity to scalp “channel,” where brain activity is viewed as the input, and the recordings on the brain-surface as the output of the channel. An evaluation of the distortion-rate function at this channel's capacity is used to obtain outer (lower) bounds on attainable mean-squared reconstruction error for localizing a single dipole. These bounds can not be surpassed using any sensing algorithm and hold in the limit of infinite number of sensors. While these limits are obtained under simplistic assumptions, these are the first limits for the problem that hold for all estimation algorithms, and need to be extended to more sophisticated models for obtaining a better understanding of optimal neural interfaces and algorithms. Finally, we also provide an upper bound on the Shannon capacity of EEG-based brain-computer interfaces.