A generalized formulation of the Linear Sampling Method with exact characterization of targets in terms of farfield measurements

Lorenzo Audibert 1, 2 Houssem Haddar 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : We propose and analyze a new formulation of the Linear Sampling Method that uses an exact characterization of the targets shape in terms of the so-called farfield operator (at a fixed frequency). This characterization is based on constructing nearby solutions of the farfield equation using minimizing sequences of a least squares cost functional with an appropriate penalty term. We first provide a general framework for the theoretical foundation of the method in the case of noise-free and noisy measurements operator. We then explicit applications for the case of inhomogeneous inclusions and indicate possible straightforward generalizations. We finally validate the method through some numerical tests and compare the performances with classical LSM and the factorization methods.
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Inverse Problems, IOP Publishing, 2014, 30 (035011), 〈10.1088/0266-5611/30/3/035011〉
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Lorenzo Audibert, Houssem Haddar. A generalized formulation of the Linear Sampling Method with exact characterization of targets in terms of farfield measurements. Inverse Problems, IOP Publishing, 2014, 30 (035011), 〈10.1088/0266-5611/30/3/035011〉. 〈hal-00911692〉

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