An Inverse Hyperbolic Problem with Application to Joint Photoacoustic Parameter Determination

TL;DR

This paper addresses an inverse hyperbolic problem motivated by photoacoustic tomography, demonstrating that a single boundary measurement can uniquely determine both wave speed and initial ultrasound pressure through their ratio.

Contribution

It introduces a novel method to recover wave speed and initial pressure from a single measurement, establishing their unique identifiability in the model.

Findings

The ratio of initial pressure to wave speed squared uniquely determines both parameters.

Single boundary measurement suffices for parameter recovery in the model.

Theoretical proof of uniqueness for the inverse problem.

Abstract

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks to recover both the wave speed and the initial ultrasound pressure from a single ultrasound signal. In particular, our result shows that the ratio of the initial ultrasound pressure and the wave speed squared uniquely determines both of them respectively.