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A time reversal algorithm in acoustic media with Dirac measure approximations

Abstract : This article is devoted to the study of a photoacoustic tomography model, where one is led to consider the solution of the acoustic wave equation with a source term writing as a separated variables function in time and space, whose temporal component is in some sense close to the derivative of the Dirac distribution at t  =  0. This models a continuous wave laser illumination performed during a short interval of time. We introduce an algorithm for reconstructing the space component of the source term from the measure of the solution recorded by sensors during a time T all along the boundary of a connected bounded domain. It is based at the same time on the introduction of an auxiliary equivalent Cauchy problem allowing to derive explicit reconstruction formula and then to use of a deconvolution procedure. Numerical simulations illustrate our approach. Finally, this algorithm is also extended to elasticity wave systems.
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https://hal.archives-ouvertes.fr/hal-01866862
Contributor : Elie Bretin Connect in order to contact the contributor
Submitted on : Monday, September 3, 2018 - 4:32:42 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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Elie Bretin, Carine Lucas, Yannick Privat. A time reversal algorithm in acoustic media with Dirac measure approximations. Inverse Problems, IOP Publishing, 2018, 34 (4), ⟨10.1088/1361-6420/aaaca9⟩. ⟨hal-01866862⟩

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