Sampling theory for spatial field sensing: Application to electro- and magnetoencephalography

Abstract: We present a theoretical framework for analyzing spatial sampling of fields in three-dimensional space. The framework bridges Shannon's sampling and information theory to Bayesian probabilistic inference and experimental design. Based on the theory, we present an approach for optimal sampling on curved surfaces and analyze spatial sampling of EEG as well as that of on- and off-scalp MEG. Our spatial-frequency analysis of simulated measurements shows that the available spatial degrees of freedom in the electric potential are limited by the smoothing due to head tissues, while those in the magnetic field are limited by the measurement distance. On-scalp MEG would generally benefit from three times more samples than EEG or off-scalp MEG. Assuming uniform whole-head sampling and similar signal-to-noise ratios, on-scalp MEG has the highest total information content among these modalities. If the number of spatial samples is small, nonuniform sampling can be beneficial.