An Information-Theoretic View of EEG Sensing
This paper uses an information-theoretic lens to examine the use and implementation of electroencephalography (EEG) systems for neural imaging. There is a widespread belief in the clinical and neuroscientific community that ultra-high-density EEG imaging of the brain (beyond the typically used few hundred or fewer electrodes) will not yield higher spatial resolution. Theoretically, this belief rests on a spatial Nyquist rate analysis for human head models. This analysis in turn relies on the understanding that high spatial frequencies (that carry high-resolution information) decay as they travel from the brain to the scalp surface. Interestingly, the belief continues to be held despite being recently challenged experimentally, in part because of the spatial Nyquist results. In this work, we question the spatial Nyquist rate analysis, mathematically as well as conceptually. Mathematically, we correct and generalize the Nyquist rate analysis, and then use it to obtain improved estimates for spatial Nyquist rates. Conceptually, we observe that the Nyquist rate analysis provides a limit on the following problem: what is the minimum number of sensors required to reconstruct the scalp EEG to within a specified (small) mean-squared error? However, this problem is fundamentally different from the imaging problem of minimizing error in reconstructing the neural source inside the brain, which optimizes a different objective, and requires inclusion of noise in the analysis. To that end, we utilize the transfer function to obtain an information-theoretic fundamental limit on the achievable accuracy in localizing single-dipole sources. The technique relies on computing the distortion-rate function for a single dipole source and evaluating it at an upper bound on mutual information across the brain-to-scalp channel, and can be extended to more general sources as well. Finally, we observe that the main obstacle in understanding the required number of EEG sensors is the lack of ultra-high-density systems that can test these limits, and information theory can prove helpful in this context as well. One engineering difficulty is that the required circuit area and energy for sampling EEG signals can be too large to enable these systems to be safe, compact, and portable. Toward reducing this area and energy, we observe that the decay of high spatial frequencies in EEG, while being a detriment to reconstruction accuracy, also leads to large spatial correlations in the recorded EEG signals. Interestingly, these correlations can be harnessed using a novel information-theoretic "hierarchical referencing" technique that can reduce circuit energy and area to enable high-resolution high-density implementations.
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