# Preconditioning Inverse Problems for Hyperbolic Equations with Applications to Photoacoustic Tomography

## TL;DR

This paper introduces a new preconditioning approach for wave equation inverse problems, enhancing robustness against regularization parameters, with potential applications in photoacoustic tomography.

## Contribution

It develops a concept for regularization parameter robust preconditioning specifically for hyperbolic inverse problems, extending ideas from elliptic control problems.

## Key findings

- Preconditioning improves stability of inverse wave problems.
- The method is applicable to photoacoustic tomography.
- Robustness against regularization parameters is achieved.

## Abstract

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning. Analogous concepts have been developed for control problems based on elliptic partial equations before.