# American Institute of Mathematical Sciences

November  2013, 7(4): 1251-1270. doi: 10.3934/ipi.2013.7.1251

## Analytic sensing for multi-layer spherical models with application to EEG source imaging

 1 École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, Switzerland 2 Chinese University of Hong Kong, Shatin, Hong Kong, China

Received  June 2011 Revised  March 2013 Published  November 2013

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.
Citation: Djano Kandaswamy, Thierry Blu, Dimitri Van De Ville. Analytic sensing for multi-layer spherical models with application to EEG source imaging. Inverse Problems & Imaging, 2013, 7 (4) : 1251-1270. doi: 10.3934/ipi.2013.7.1251
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