WIAS Preprint No. 943, (2004)
A regularized Newton method in electrical impedance tomography using shape Hessian information
Authors
- Eppler, Karsten
- Harbrecht, Helmut
2010 Mathematics Subject Classification
- 49Q10 49M37 65N38 49K20
Keywords
- electrical impedance tomography, shape optimization, integral equation method, Newton type descent
DOI
Abstract
The present paper is concerned with the identification of an obstacle or void of different conductivity included in a two-dimensional domain by measurements of voltage and currents at the boundary. We employ a reformulation of the given identification problem as a shape optimization problem as proposed by Sokolowski and Roche. It turns out that the shape Hessian degenerates at the given hole which gives a further hint on the ill-posedness of the problem. For numerical methods, we propose a preprocessing for detecting the barycenter and a crude approximation of the void or hole. Then, we resolve the shape of the hole by a regularized Newton method.
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