A global stability estimate for the photo-acoustic inverse problem in layered media

TL;DR

This paper establishes global stability estimates for reconstructing optical properties in layered media using photoacoustic imaging, quantifying how stability diminishes with depth.

Contribution

It provides the first rigorous global Hölder stability estimates for the photoacoustic inverse problem in layered media with known acoustic speed.

Findings

Stability is strong near the illumination source.

Stability deteriorates exponentially with depth.

Results align with experimental resolution limits.

Abstract

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global H\"{o}lder stability estimates of the photo-acoustic inversion. These results show that the reconstruction is stable in the region close to the optical illumination source, and deteriorate exponentially far away. Several experimental pointed out that the resolution depth of the photo-acoustic modality is about tens of millimeters. Our stability estimates confirm these observations and give a rigorous quantification of this depth resolution.