On an inverse problem in photoacoustic

TL;DR

This paper investigates the inverse problem of reconstructing Cauchy data for the wave equation in two and three dimensions using boundary measurements on a unit ball, contributing to the mathematical understanding of photoacoustic imaging.

Contribution

It provides new theoretical insights into reconstructing wave equation data from boundary measurements in photoacoustic problems.

Findings

Established conditions for unique reconstruction.

Derived explicit formulas for the inverse problem.

Extended analysis to both 2D and 3D cases.

Abstract

We consider the problem of reconstruction of the Cauchy data for the wave equation in $\mathbb{R}^3$ and $\mathbb{R}^2$ by the measurements of its solution on the boundary of the unit ball.