Recovery of an inclusion in Photoacoustic imaging

TL;DR

This paper demonstrates that a star-shaped inclusion within biological tissue can be uniquely identified and stably reconstructed using a single boundary measurement in photoacoustic imaging, assuming piecewise constant properties.

Contribution

It introduces a novel approach assuming piecewise constant parameters and establishes uniqueness and Lipschitz stability for the inclusion recovery from a single measurement.

Findings

Unique recovery of the inclusion from one measurement

Lipschitz stability estimate for the inversion

New observability inequality for wave equations with piecewise constant speed

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.