Mohamed Jaoua ; Slim Chaabane ; Chokri Elhechmi ; Juliette Leblond ; Moncef Mahjoub et al. - On some robust algorithms for the Robin inverse problem

arima:1903 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, August 21, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 -
On some robust algorithms for the Robin inverse problemArticle

Authors: Mohamed Jaoua 1; Slim Chaabane 2; Chokri Elhechmi 2; Juliette Leblond 3; Moncef Mahjoub 4; Jonathan R. Partington 4

  • 1 Laboratoire Jean Alexandre Dieudonné [LJAD]
  • 2 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
  • 3 Analysis and Problems of Inverse type in Control and Signal processing
  • 4 School of Computing [Leeds]

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.

Volume: Volume 9, 2007 Conference in Honor of Claude Lobry, 2008
Published on: August 21, 2008
Submitted on: January 24, 2008
Keywords: Inverse problems, Cauchy problem, Robin coefficient, Stability, Hardy classes, Recovery algorithms,Problèmes inverses,Problème de Cauchy,Coefficient de Robin,Stabilité,Algorithmes d’identification,[INFO] Computer Science [cs],[MATH] Mathematics [math]

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