May  2009, 3(2): 353-371. doi: 10.3934/ipi.2009.3.353

A Newton method for reconstructing non star-shaped domains in electrical impedance tomography

1. 

Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany

2. 

Institut für Numerische und Angewandte Mathematik, Lotzestr. 16-18 D-37083 Göttingen

Received  January 2009 Revised  March 2009 Published  May 2009

We study the reconstruction of the shape of a perfectly conducting inclusion in three dimensional electrical impedance tomography (EIT) using a regularized Newton method. This method involves a least squares penalty in the form of an additional nonlinear operator to cope with the non-uniqueness of general parametrizations of the unknown boundary. We provide a convergence result for this method in the general framework of nonlinear ill-posed operator equations. Moreover, we discuss the evaluation of the forward operator in EIT, its derivative, and the adjoint of the derivative using a wavelet based boundary element method. Numerical examples illustrate the performance of our method.
Citation: Helmut Harbrecht, Thorsten Hohage. A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Inverse Problems & Imaging, 2009, 3 (2) : 353-371. doi: 10.3934/ipi.2009.3.353
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