Recovery of an inclusion in photoacoustic imaging

Yavar Kian; Faouzi Triki

doi:10.3934/ipi.2024050

Article Contents

2025, Volume 19, Issue 4: 693-714. Doi: 10.3934/ipi.2024050

This issue Previous Article Quantum computing algorithms for inverse problems on graphs and an NP-complete inverse problem Next Article On some analytic properties of the atmospheric tomography operator: Non-Uniqueness and reconstructability issues

Recovery of an inclusion in photoacoustic imaging

Yavar Kian^1, , and
Faouzi Triki^{1, 2,}

1.
Univ Rouen Normandie, CNRS, Normandie Univ, LMRS UMR 6085, F-76000 Rouen, France
2.
Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin- d'Hères, France

^*Corresponding author: Yavar Kian
^*Corresponding author: Yavar Kian

Received: August 2024

Revised: November 2024

Early access: December 13, 2024

Published online: December 13, 2024

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Abstract

In photoacoustic imaging the objective is to determine the optical properties of biological tissue from boundary measurement of the generated acoustic wave. Here, we propose a restriction to piecewise constant media parameters. Precisely we assume that the acoustic speed and the optical coefficients take two different constants inside and outside a star shaped inclusion. We show that the inclusion can be uniquely recovered from a single measurement corresponding to measurement of the pressure for one pair of unknown data at the boundary of the domain along the time interval. We also derive a stability estimate of Lipschitz type of the inversion. The proof of stability is based on an integral representation and a new observability inequality for the wave equation with piecewise constant speed that is of interest itself.

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Mathematics Subject Classification: Primary: 35R30, 35L05.

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