Recovery of an inclusion in photoacoustic imaging
Year: 2024
Type: article
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.
Source: Inverse Problems and Imaging
DOI: 10.3934/ipi.2024050
Authors: Yavar Kian, Faouzi Triki
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405409996