Parametrix for the inverse source problem of thermoacoustic tomography with reduced data

Abstract: We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Our goal is to find efficient non-iterative solutions to this problem.

I will present two different methods:

(1) A procedure based on solving the exterior Dirichlet problem and computing the Radon transform of the solution. This technique works under assumption of a constant speed of sound.

(2) A procedure based on modifying the time-reversed solution by two Hilbert transforms, one in time and one in a certain spatial variable. This techniques works for a smooth known speed of sound, subject to an additional geometric condition.

Both techniques produce microlocally accurate approximations to the sought initial condition. In certain geometries these methods can be implemented as fast algorithms. Performance of these techniques will be demonstrated in numerical simulations.

Joint work with M. Eller and P. Hoskins

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine