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An inverse hyperbolic problem with application to joint photoacoustic parameter determination

Shitao Liu, Gunther Uhlmann and Yang Yang
Vol. 8 (2026), No. 2, 477–495
DOI: 10.2140/paa.2026.8.477
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.

Keywords
inverse hyperbolic problem, Carleman estimate, single boundary measurement, photoacoustic tomography
Mathematical Subject Classification
Primary: 35R30
Secondary: 35L05
Milestones
Received: 30 August 2024
Revised: 15 January 2025
Accepted: 28 May 2026
Published: 12 July 2026
Authors
Shitao Liu
School of Mathematical and Statistical Sciences
Clemson University
Clemson, SC
United States
Gunther Uhlmann
Department of Mathematics
University of Washington
Seattle, WA
United States
Yang Yang
Department of Computational Mathematics, Science and Engineering
Michigan State University
East Lansing, MI
United States
© 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).