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Journal of Inverse and Ill-posed Problems

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Volume 25, Issue 6


Quantitative thermoacoustic tomography with microwaves sources

Hassan Akhouayri / Maïtine Bergounioux
  • Corresponding author
  • University of d’Orléans, Laboratory MAPMO, CNRS, UMR 7349,Fédération Denis Poisson, FR 2964, Bâtiment de Mathématiques, BP 6759, 45067 Orléans cedex 2, France
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/ Anabela Da Silva / Peter Elbau / Amelie Litman / Leonidas Mindrinos
Published Online: 2016-12-02 | DOI: https://doi.org/10.1515/jiip-2016-0012


We investigate a quantitative thermoacoustic tomography process. We aim to recover the electric susceptibility and the conductivity of a medium when the sources are in the microwaves range. We focus on the case where the source signal has a slow time-varying envelope. We present the direct problem coupling equations for the electric field, the temperature variation and the pressure (to be measured via sensors). Then we give a variational formulation of the inverse problem which takes into account the entire electromagnetic, thermal and acoustic coupled system, and perform the formal computation of the optimality system.

Keywords: Thermoacoustic tomography; inverse problem; optimal control; Maxwell’s equations

MSC 2010: 35M33; 35Q61; 49N45; 80A23; 93C20


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About the article

Received: 2016-02-05

Revised: 2016-10-10

Accepted: 2016-11-03

Published Online: 2016-12-02

Published in Print: 2017-12-01

Funding Source: Agence Nationale de la Recherche

Award identifier / Grant number: ANR-12-BLAN-BS01-0001-01

Funding Source: OeAD-GmbH

Award identifier / Grant number: WTZ FR14/2013

This work is supported by ANR (AVENTURES – ANR-12-BLAN-BS01-0001-01) and Partenariat Hubert Curien AMADEUS, OEAD WTZ FR14/2013.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 6, Pages 703–717, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2016-0012.

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