Multiwave tomography in a closed domain: averaged sharp time reversal

TL;DR

This paper introduces an averaged sharp time reversal algorithm for multiwave tomography in a closed domain with boundary reflections, providing explicit solutions and parametrices depending on measurement coverage.

Contribution

It develops a novel averaged sharp time reversal method for multiwave tomography with boundary reflections, including explicit solutions and parametrices for partial boundary data.

Findings

Explicit solution via Neumann series for full boundary measurements

Parametrix construction for partial boundary measurements

Effective handling of wave reflections in a closed domain

Abstract

We study the mathematical model of multiwave tomography including thermo and photoacoustic tomography with a variable speed for a fixed time interval $[0,T]$. We assume that the waves reflect from the boundary of the domain. We propose an averaged sharp time reversal algorithm. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. When the measurements are taken on a part of the boundary, we show that the same algorithm produces a parametrix.