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Tailored interior and boundary parameter transformations for iterative inversion in electrical impedance tomography

Winkler, Robert

Abstract:
Electrical impedance tomography is a non-invasive method for imaging the electrical conductivity of an object from electrode measurements on its surface. The underlying mathematical problem is highly nonlinear, severely ill-posed, and several model parameters are usually not known accurately. Despite the strong nonlinearity, iterative Newton-type methods are widely used to tackle the problem numerically. This work presents and analyzes tailored transformations for the conductivity and for electrode parameters which are favourable in two regards: they remove the constrainedness of the unknown parameters and simultaneously decrease the nonlinearity of the underlying problem. We study the impact of various transformations on the nonlinearity of the problem and demonstrate improved speed of convergence for Newton-type methods while avoiding local minima in the solution space. The presented transformations can conveniently be incorporated into existing iterative solvers as they improve stability and do not require hand-tuned regularization parameters or line-search strategies, thereby bridging a gap between a variety of established conductivity estimation methods and practical applications.

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Verlagsausgabe §
DOI: 10.5445/IR/1000117662
Veröffentlicht am 11.03.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 11.2019
Sprache Englisch
Identifikator ISSN: 0266-5611, 1361-6420
KITopen-ID: 1000117662
Erschienen in Inverse problems
Band 35
Heft 11
Seiten Art. Nr.: 114007
Vorab online veröffentlicht am 04.10.2019
Schlagwörter electrical impedance tomography, parameter transformation, electrode geometry, nonlinearity, constrainedness, iterative inversion, Newton method
Nachgewiesen in Scopus
Web of Science
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