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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.
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Maïtine Bergounioux, Xavier Bonnefond, Thomas Haberkorn, Yannick Privat. An optimal control problem in photoacoustic tomography. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, 24 (12), pp.2525--2548. ⟨10.1142/S0218202514500286⟩. ⟨hal-00833867v2⟩

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