 |
Journal articles
An optimal control problem in photoacoustic tomography
Abstract : This article is devoted to the introduction and study of a photoacoustic tomography model, an imaging technique based on the reconstruction of an internal photoacoustic source distribution from measurements acquired by scanning ultrasound detectors over a surface that encloses the body containing the source under study. In a nutshell, the inverse problem consists in determining absorption and diffusion coefficients in a system coupling a hyperbolic equation (acoustic pressure wave) with a parabolic equation (diffusion of the fluence rate), from boundary measurements of the photoacoustic pressure. Since such kinds of inverse problems are known to be generically ill-posed, we propose here an optimal control approach, introducing a penalized functional with a regularizing term in order to deal with such difficulties. The coefficients we want to recover stand for the control variable. We provide a mathematical analysis of this problem, showing that this approach makes sense. We finally write necessary first order optimality conditions and give preliminary numerical results.
Cited literature [37 references]
https://hal.archives-ouvertes.fr/hal-00833867
Contributor : Yannick Privat <>
Submitted on : Saturday, March 1, 2014 - 9:18:46 AM
Last modification on : Friday, March 27, 2020 - 3:12:48 AM
Document(s) archivé(s) le : Friday, May 30, 2014 - 3:50:36 PM
Contributor : Yannick Privat <>
Submitted on : Saturday, March 1, 2014 - 9:18:46 AM
Last modification on : Friday, March 27, 2020 - 3:12:48 AM
Document(s) archivé(s) le : Friday, May 30, 2014 - 3:50:36 PM
File
BBHPrev_Hal.pdf
Files produced by the author(s)
Licence
Distributed under a Creative Commons Attribution 4.0 International License
