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An optimal control problem in photoacoustic tomography

M. Bergounioux,Xavier Bonnefond,T. Haberkorn,Y. Privat

Published 2014 in Mathematical Models and Methods in Applied Sciences

ABSTRACT

This paper 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.

PUBLICATION RECORD

  • Publication year

    2014

  • Venue

    Mathematical Models and Methods in Applied Sciences

  • Publication date

    2014-08-15

  • Fields of study

    Mathematics, Physics, Engineering

  • Identifiers
    DOI 10.1142/S0218202514500286
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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