Stability for Quantitative Photoacoustic Tomography with well chosen illuminations

TL;DR

This paper establishes stable methods for recovering optical properties in 3D Quantitative Photoacoustic Tomography using specially chosen illuminations, eliminating the need for difficult nondegeneracy conditions.

Contribution

It introduces universal illumination strategies that ensure Hölder stability in recovering diffusion and absorption coefficients without prior nondegeneracy assumptions.

Findings

Universal illumination choices enable stable coefficient recovery

Stability achieved without nondegeneracy conditions

Applicable to three-dimensional QPAT imaging

Abstract

We treat the stability issue for the three dimensional inverse imaging modality called Quantitative Photoacoustic Tomography. We provide universal choices of the illuminations which enable to recover, in a H\"older stable fashion, the diffusion and absorption coefficients from the interior pressure data. With such choices of illuminations we do not need the nondegeneracy conditions commonly used in previous studies, which are difficult to be verified a-priori.