An improved time domain linear sampling method for Robin and Neumann obstacles

Houssem Haddar 1 Armin Lechleiter 2 Simon Marmorat 3
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
3 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 : We consider inverse obstacle scattering problems for the wave equation with Robin or Neu- mann boundary conditions. The problem of reconstructing the geometry of such obstacles from measurements of scattered waves in the time domain is tackled using a time domain linear sampling method. This imaging technique yields a picture of the scatterer by solving a linear operator equation involving the measured data for many right-hand sides given by singular so- lutions to the wave equation. We analyze this algorithm for causal and smooth impulse shapes, we discuss the effect of different choices of the singular solutions used in the algorithm, and finally we propose a fast FFT-based implementation.
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Houssem Haddar, Armin Lechleiter, Simon Marmorat. An improved time domain linear sampling method for Robin and Neumann obstacles. Applicable Analysis, Taylor & Francis, 2013, pp.1-22. ⟨10.1080/00036811.2013.772583⟩. ⟨hal-00768725⟩

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