An improved time domain linear sampling method for Robin and Neumann obstacles |
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Authors: | Houssem Haddar Armin Lechleiter Simon Marmorat |
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Affiliation: | 1. DEFI, INRIA Saclay-Ile-de-France and CMAP, Ecole Polytechnique, 91128 Palaiseau, France.haddar@cmapx.polytechnique.fr;3. Center for Industrial Mathematics, University of Bremen, 28359 Bremen, Germany.;4. POEMS, INRIA Rocquencourt, 78153 Le Chesnay, France. |
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Abstract: | We consider inverse obstacle scattering problems for the wave equation with Robin or Neumann 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 solutions to the wave equation. We analyse 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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Keywords: | Inverse scattering time domain linear sampling method retarded potentials |
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