# Photo-acoustic tomography in a rotating setting

## TL;DR

This paper develops a direct inversion method for photo-acoustic tomography in a rotating setup, demonstrating unique recovery and optimal stability of optical parameters without relying on traditional two-step procedures.

## Contribution

It introduces a novel direct inversion approach for rotating photo-acoustic tomography, modeling the process as a composition of pseudo-differential and Fourier integral operators, and proves injectivity and stability.

## Key findings

- Unique reconstruction of optical coefficients in rotating setting
- Establishment of optimal stability estimates
- Extension of standard non-rotating results to rotating configurations

## Abstract

Photo-acoustic tomography is a coupled-physics (hybrid) medical imaging modality that aims to reconstruct optical parameters in biological tissues from ultrasound measurements. As propagating light gets partially absorbed, the resulting thermal expansion generates minute ultrasonic signals (the photo-acoustic effect) that are measured at the boundary of a domain of interest. Standard inversion procedures first reconstruct the source of radiation by an inverse ultrasound (boundary) problem and second describe the optical parameters from internal information obtained in the first step. This paper considers the rotating experimental setting. Light emission and ultrasound measurements are fixed on a rotating gantry, resulting in a rotation-dependent source of ultrasound. The two-step procedure we just mentioned does not apply. Instead, we propose an inversion that directly aims to reconstruct the optical parameters quantitatively. The mapping from the unknown (absorption and diffusion) coefficients to the ultrasound measurement via the unknown ultrasound source is modeled as a composition of a pseudo-differential operator and a Fourier integral operator. We show that for appropriate choices of optical illuminations, the above composition is an elliptic Fourier integral operator. Under the assumption that the coefficients are unknown on a sufficiently small domain, we derive from this a (global) injectivity result (measurements uniquely characterize our coefficients) combined with an optimal stability estimate. The latter is the same as that obtained in the standard (non-rotating experimental) setting.