Gradual time reversal in thermo- and photo-acoustic tomography within a resonant cavity

B. Holman, L. Kunyansky

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods (including the popular time reversal algorithm) cannot be used. The inverse problem involving reflecting walls can be solved by the gradual time reversal method we propose here. It consists in solving back in time on the interval the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

Original languageEnglish (US)
Article number035008
JournalInverse Problems
Volume31
Issue number3
DOIs
StatePublished - Mar 1 2015

Keywords

  • photoacoustic tomography
  • reflecting walls
  • resonant cavity
  • thermoacoustic tomography
  • time reversal
  • wave equation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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