Location of Repository

An optimal control problem in photoacoustic tomography

By Maïtine Bergounioux, Xavier Bonnefond, Thomas Haberkorn and Yannick Privat


International audienceThis 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

Topics: Photoacoustic tomography, inverse problem, optimal control, 49J20, 35M33, 80A23, 93C20, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]
Publisher: World Scientific Publishing
Year: 2014
DOI identifier: 10.1142/S0218202514500286
OAI identifier: oai:HAL:hal-00833867v2
Provided by: Hal-Diderot

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.