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On some robust algorithms for the Robin inverse problem

Abstract : The problem we are dealing with is to recover a Robin coefficient (or impedance) from measurements performed on some part of the boundary of a domain, in the framework of nondestructive testing by the means of Electric Impedance Tomography. The impedance can provide information on the location of a corroded area, as well as on the extent of the damage, which has possibly occurred on an unaccessible part of the boundary. Two different identification algorithms are presented and studied: the first one is based on a Kohn and Vogelius cost function, actually an energetic least squares one, which turns the inverse problem into an optimization one ; as for the second, it makes use of the best approximation in Hardy classes, in order to extend the Cauchy data to the unreachable part of the boundary, and then compute the Robin coefficient from these extended data. Special focus is put on the robustness with respect to noise, both from a mathematical and and numerical point of view. Some numerical experiments are eventually presented and compared.
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Mohamed Jaoua, Slim Chaabane, Chokri Elhechmi, Juliette Leblond, Moncef Mahjoub, et al.. On some robust algorithms for the Robin inverse problem. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2008, 9, pp.287-307. ⟨hal-01277781⟩

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