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Theses

Modeling and simulation in photoacoustics

Abstract : This thesis deals with the problem of photoacoustic imaging. In this imaging setting, one heats a medium up with an electromagnetic wave. The medium dilates and emits an ultrasonic wave. The aim is then to reconstruct inner properties of the medium from boundary measurements. It is an inverse problem on the initial condition for the wave equation. In an idealized frame, the reconstruction procedure has been thoroughly studied. The main goal of this thesis is to stray from the standard model by considering less restrictive assumptions. For each of them (boundary condition, partial view, attenuation, inhomogeneous sound speed) the thesis proposes a correction based on adapted mathematical tools (asymptotic analysis, dual approach , correlation...). Reconstruction of the initial condition of the wave equation is however not enough. It depends on the electromagnetique illumination. A second inverse problem has to be solved on the electromagnetic wave propagation to acces the physical coefficients of interest. The thesis presents algorithmic results in the frame of the diffusion equation and theoretic estimates in the frame of the transport equation. The thesis also presents an improving result for a topological derivative based imaging approach.
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Contributor : Vincent Jugnon <>
Submitted on : Monday, December 13, 2010 - 1:56:10 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
Long-term archiving on: : Monday, March 14, 2011 - 3:05:15 AM

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Vincent Jugnon. Modeling and simulation in photoacoustics. Analysis of PDEs [math.AP]. Ecole Polytechnique X, 2010. English. ⟨pastel-00545973⟩

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