Determining planar multiple sound-soft obstacles from scattered acoustic fields

A. Carpio, B.T. Johansson, M.-L. Rapún

Research output: Contribution to journalArticle

Abstract

An inverse problem is considered where the structure of multiple sound-soft planar obstacles is to be determined given the direction of the incoming acoustic field and knowledge of the corresponding total field on a curve located outside the obstacles. A local uniqueness result is given for this inverse problem suggesting that the reconstruction can be achieved by a single incident wave. A numerical procedure based on the concept of the topological derivative of an associated cost functional is used to produce images of the obstacles. No a priori assumption about the number of obstacles present is needed. Numerical results are included showing that accurate reconstructions can be obtained and that the proposed method is capable of finding both the shapes and the number of obstacles with one or a few incident waves.
Original languageEnglish
Pages (from-to)185-199
Number of pages15
JournalJournal of Mathematical Imaging and Vision
Volume36
Issue number2
Early online date16 Dec 2009
DOIs
Publication statusPublished - Feb 2010

Keywords

  • shape reconstruction
  • topological derivative
  • scattering
  • sound-soft obstacles
  • acoustic waves

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