A time reversal algorithm in acoustic media with Dirac measure approximations. (26th February 2018)

• Record Type: Journal Article
• Authors: Bretin, Élie; Lucas, Carine; Privat, Yannick
• Is Part Of: Inverse problems. Volume 34:Number 4(2018:Apr.)
• Publication Date: 2018-02-26
• Subjects: wave system -- elasticity system -- time reversal method -- Fourier analysis -- photoacoustic imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaaca9
• Languages: English
• ISSNs: 0266-5611

Abstract

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.