A time reversal algorithm in acoustic media with Dirac measure approximations

Élie Bretin (1) , Carine Lucas (2) , Yannick Privat (3)

1 MMCS - Modélisation mathématique, calcul scientifique
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 LJLL - Laboratoire Jacques-Louis Lions

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.

Domaines: Equations aux dérivées partielles [math.AP]

Élie Bretin, Carine Lucas, Yannick Privat. A time reversal algorithm in acoustic media with Dirac measure approximations. Inverse Problems, 2018, 34 (4). ⟨hal-01529580v2⟩