Inverse source problems for eddy current equations

We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we...

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Bibliographic Details
Published inInverse problems Vol. 28; no. 1; pp. 015006 - 15
Main Authors Rodríguez, Ana Alonso, Camaño, Jessika, Valli, Alberto
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2012
Institute of Physics
Subjects
Approximation
Boundaries
Brain
eddy current equations
Eddy currents
electroencephalography
Electromagnetic fields
Exact sciences and technology
Inverse
inverse source problem
magnetoencephalography
Mathematical analysis
Maxwell equation
Physics
Inverse problems
Dipoles
Electromagnetic fields
Localization
Maxwell equations
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Summary:We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources. On the other hand, we prove that the inverse source problem has a unique solution if the source is supported on the boundary of a subdomain or if it is the sum of a finite number of dipoles. We address the applicability of this result for the localization of brain activity from electroencephalography and magnetoencephalography measurements.
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ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/28/1/015006