Time reversal method with stabilizing boundary conditions for Photoacoustic tomography

TL;DR

This paper introduces a modified time reversal method with stabilizing boundary conditions for Photoacoustic tomography, demonstrating exponential convergence with partial boundary data in noiseless scenarios.

Contribution

It proposes a novel modification of the back and forth nudging method that ensures exponential convergence under natural visibility conditions.

Findings

Method converges exponentially under certain conditions

Effective with partial boundary data

Applicable to noiseless measurements

Abstract

We study an inverse initial source problem that models Photoacoustic tomography measurements with array detectors, and introduce a method that can be viewed as a modification of the so called back and forth nudging method. We show that the method converges at an exponential rate under a natural visibility condition, with data given only on a part of the boundary of the domain of wave propagation. In this paper we consider the case of noiseless measurements.