Recovery of an inclusion in Photoacoustic imaging

Yavar Kian; Faouzi Triki

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arXiv · 2407.05317

Recovery of an inclusion in Photoacoustic imaging

Yavar Kian·Faouzi Triki

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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. 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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Yavar Kian, Faouzi Triki. 2024-07-07. Recovery of an inclusion in Photoacoustic imaging. https://arxiv.org/abs/2407.05317

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