A dissipative time reversal technique for photoacoustic tomography in a cavity

Linh V. Nguyen, Leonid A. Kunyansky

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We consider the inverse source problem arising in thermo- and photoacoustic tomography. It consists in reconstructing the initial pressure from the boundary measurements of the acoustic wave. Our goal is to extend versatile time reversal techniques to the case when the boundary of the domain is perfectly reecting, effectively turning the domain into a reverberant cavity. Standard time reversal works only if the solution of the direct problem decays in time, which does not happen in the setup we consider. We thus propose a novel time reversal technique with a nonstandard boundary condition. The error induced by this time reversal technique satisfies the wave equation with a dissipative boundary condition and, therefore, decays in time. For larger measurement times, this method yields a close approximation; for smaller times, the first approximation can be iteratively refined, resulting in a convergent Neumann series for the approximation.

Original languageEnglish (US)
Pages (from-to)748-769
Number of pages22
JournalSIAM Journal on Imaging Sciences
Volume9
Issue number2
DOIs
StatePublished - May 26 2016

Keywords

  • Cavity
  • Geometric control condition
  • Photoacoustic tomography
  • Thermoacoustic tomography
  • Time reversal

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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