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

Djano Kandaswamy; Thierry Blu; Dimitri Van De Ville

doi:10.3934/ipi.2013.7.1251

Article Contents

2013, Volume 7, Issue 4: 1251-1270. Doi: 10.3934/ipi.2013.7.1251

This issue Previous Article Multi-wave imaging in attenuating media Next Article Factorization method for the inverse Stokes problem

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

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

Received: June 2011

Revised: March 2013

Published online: November 2013

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 15A29, 35J05, 31B20; Secondary: 94A12, 94A20, 15A18.

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