A Dissipative Time Reversal Technique for Photoacoustic Tomography in a Cavity
AffiliationUniv Arizona, Dept Math
geometric control condition
MetadataShow full item record
CitationA Dissipative Time Reversal Technique for Photoacoustic Tomography in a Cavity 2016, 9 (2):748 SIAM Journal on Imaging Sciences
JournalSIAM Journal on Imaging Sciences
Rights© 2016, Society for Industrial and Applied Mathematics.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractWe 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.
VersionFinal published version
SponsorsNSF/DMS award [1212125, 1211521]