A fast reconstruction algorithm for geometric inverse problems using topological sensitivity analysis and Dirichlet-Neumann cost functional approach
Abstract
This paper is concerned with the detection of objects immersed in anisotropic media from boundary measurements. We propose an accurate approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The inverse problem is formulated as a topology optimization one minimizing an energy like functional. A topological asymptotic expansion is derived for the anisotropic Laplace operator. The unknown object is reconstructed using a level-set curve of the topological gradient. The efficiency and accuracy of the proposed algorithm are illustrated by some numerical results. MOTS-CL\'ES : Probl\`eme inverse g\'eom\'etrique, Laplace anisotrope, formulation de Kohn-Vogelius, analyse de sensibilit\'e, optimisation topologique.
Cite
@article{arxiv.1707.03589,
title = {A fast reconstruction algorithm for geometric inverse problems using topological sensitivity analysis and Dirichlet-Neumann cost functional approach},
author = {Maatoug Hassine and Imen Kallel},
journal= {arXiv preprint arXiv:1707.03589},
year = {2017}
}