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Recovery of an inclusion in Photoacoustic imaging

Authors :
Kian, Yavar
Triki, Faouzi
Publication Year :
2024

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.

Subjects

Subjects :
Mathematics - Analysis of PDEs

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2407.05317
Document Type :
Working Paper