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A global stability estimate for the photo-acoustic inverse problem in layered media

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  17 May 2018

KUI REN  and
FAOUZI TRIKI
KUI REN
Affiliation:
Department of Mathematics and Institute of Computational Engineering and Sciences (ICES), The University of Texas, Austin, TX 78712, USA email: ren@math.utexas.edu
FAOUZI TRIKI
Affiliation:
Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin-d'Hères, France email: faouzi.triki@univ-grenoble-alpes.fr
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Abstract

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known, we derive global Hölder stability estimates of the photoacoustic inversion. These results show that the reconstruction is stable in the region close to the optical illumination source, and deteriorate exponentially far away. Several experimental pointed out that the resolution depth of the photoacoustic modality is about tens of millimeters. Our stability estimates confirm these observations and give a rigorous quantification of this depth resolution.

Keywords

Inverse problemswave equationdiffusion equationLipschitz stability

MSC classification

Primary: 35R30: Inverse problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 3 , June 2019 , pp. 505 - 528
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

The research of FT was supported in part by grant LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) and grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde).

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