# Analysis of the Linearized Problem of Quantitative Photoacoustic Tomography

## TL;DR

This paper investigates the linearized inverse problem in quantitative photoacoustic tomography using the radiative transfer equation, providing stability, uniqueness results, and numerical evidence that linearization yields accurate and computationally efficient reconstructions.

## Contribution

It derives stability and uniqueness results for the linearized problem in photoacoustic tomography using radiative transfer, and demonstrates the effectiveness of linearization through numerical simulations.

## Key findings

- Linearized problem is stable and unique under certain conditions.
- Numerical simulations confirm the stability and accuracy of the linearized approach.
- Linearization significantly reduces computational cost while maintaining accuracy.

## Abstract

Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative transfer equation as accurate model for light transport. As main theoretical results, we derive several stability and uniqueness results for the linearized inverse problem. We consider the case of single illumination as well as the case of multiple illuminations assuming full or partial data. The numerical solution of the linearized problem is much less costly than the solution of the non-linear problem. We present numerical simulations supporting the stability results for the linearized problem and demonstrate that the linearized problem already gives accurate quantitative results.