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A time reversal algorithm in acoustic media with Dirac measure approximations. (English) Zbl 1388.35221

Summary: 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.

MSC:

35R30 Inverse problems for PDEs
35Q35 PDEs in connection with fluid mechanics
92C55 Biomedical imaging and signal processing
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