Return to search

A Dissipative Time Reversal Technique for Photoacoustic Tomography in a Cavity

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 reflecting, 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.

Identiferoai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/622000
Date01 1900
CreatorsNguyen, Linh V., Kunyansky, Leonid A.
ContributorsUniv Arizona, Dept Math
PublisherSIAM PUBLICATIONS
Source SetsUniversity of Arizona
LanguageEnglish
Detected LanguageEnglish
TypeArticle
Rights© 2016, Society for Industrial and Applied Mathematics
Relationhttp://epubs.siam.org/doi/10.1137/15M1049683

Page generated in 0.0019 seconds