Analytic Sensing For Multi-Layer Spherical Models With Application To EEG Source Imaging
Source imaging maps back boundary measurements to underlying generators within the domain; e. g., retrieving the parameters of the generating dipoles from electrical potential measurements on the scalp such as in electroencephalography (EEG). Fitting such a parametric source model is non-linear in the positions of the sources and renewed interest in mathematical imaging has led to several promising approaches. One important step in these methods is the application of a sensing principle that links the boundary measurements to volumetric information about the sources. This principle is based on the divergence theorem and a mathematical test function that needs to be an homogeneous solution of the governing equations (i.e., Poisson's equation). For a specific choice of the test function, we have devised an algebraic non-iterative source localization technique for which we have coined the term "analytic sensing". Until now, this sensing principle has been applied to homogeneous-conductivity spherical models only. Here, we extend it for multi-layer spherical models that are commonly applied in EEG. We obtain a closed-form expression for the test function that can then be applied for subsequent localization. A simulation study show the feasibility of the proposed approach.