# Photoacoustic image reconstruction from full field data in heterogeneous media

## TL;DR

This paper advances photoacoustic image reconstruction by introducing novel one-step methods that handle variable sound speed, improving stability and accuracy over traditional two-step approaches, supported by numerical comparisons.

## Contribution

It presents new one-step reconstruction algorithms for full-field photoacoustic tomography that incorporate variable sound speed, enhancing existing methods.

## Key findings

- One-step methods improve reconstruction stability.
- Numerical results show better accuracy than two-step approaches.
- Handling variable sound speed enhances real-world applicability.

## Abstract

We consider image reconstruction in full-field photoacoustic tomography, where 2D projections of the full 3D acoustic pressure distribution at a given time T>0 are collected. We discuss existing results on the stability and uniqueness of the resulting image reconstruction problem and review existing reconstruction algorithms. Open challenges are also mentioned. Additionally, we introduce novel one-step reconstruction methods allowing for a variable speed of sound. We apply preconditioned iterative and variational regularization methods to the one-step formulation. Numerical results using the one-step formulation are presented, together with a comparison with the previous two-step approach for full-field photoacoustic tomography