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.
https://hal.archives-ouvertes.fr/hal-00833867 Contributor : Yannick PrivatConnect in order to contact the contributor Submitted on : Saturday, March 1, 2014 - 9:18:46 AM Last modification on : Tuesday, November 16, 2021 - 4:55:36 AM Long-term archiving on: : Friday, May 30, 2014 - 3:50:36 PM
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⟩