The Factorization Method for Electrical Impedance Tomography in the Half-Space
We consider the inverse problem of electrical impedance tomography in a conducting half-space, given electrostatic measurements on its boundary, i. e., a hyperplane. We first provide a rigorous weak analysis of the corresponding forward problem and then develop a numerical algorithm to solve an asso...
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Veröffentlicht in: | SIAM journal on applied mathematics 2008-01, Vol.68 (4), p.907-924 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We consider the inverse problem of electrical impedance tomography in a conducting half-space, given electrostatic measurements on its boundary, i. e., a hyperplane. We first provide a rigorous weak analysis of the corresponding forward problem and then develop a numerical algorithm to solve an associated inverse problem. This inverse problem consists of the reconstruction of certain inclusions within the half-space which have a different conductivity than the background. To solve the inverse problem we employ the so-called factorization method of Kirsch, which so far has only been considered for the impedance tomography problem in bounded domains. Our analysis of the forward problem makes use of a Liouville-type argument which says that a harmonic function in the entire two-dimensional plane must be a constant if some weighted L²-norm of this function is bounded. |
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ISSN: | 0036-1399 1095-712X |
DOI: | 10.1137/06067064X |