Inverse acoustic scattering using high-order small-inclusion expansion of misfit function

Marc Bonnet 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems involving the identification of penetrable obstacles, whereby the featured data-misfit cost function J is expanded in powers of the characteristic radius a of a single small inhomo-geneity. The O(a 6) approximation J 6 of J is derived and justified for a single obstacle of given location, shape and material properties embedded in a 3D acoustic medium of arbitrary shape. The generalization of J 6 to multiple small obstacles is outlined. Simpler and more explicit expressions of J 6 are obtained when the scatterer is centrally-symmetric or spherical. An approximate and computationally light global search procedure, where the location and size of the unknown object are estimated by minimizing J 6 over a search grid, is proposed and demonstrated on numerical experiments, where the identification from known acoustic pressure on the surface of a penetrable scatterer embedded in a acoustic semi-infinite medium, and whose shape may differ from that of the trial obstacle assumed in the expansion of J, is considered.
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Marc Bonnet. Inverse acoustic scattering using high-order small-inclusion expansion of misfit function. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2018, 12 (4), pp.921-953. ⟨10.3934/ipi.2018039⟩. ⟨hal-01828087⟩

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