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An optimal control problem in photoacoustic tomography

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

Abstract

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

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