# Thermoacoustic Tomography with Circular Integrating Detectors and Variable Wave Speed

## TL;DR

This paper investigates the mathematical properties of thermoacoustic tomography with circular detectors under variable wave speed, analyzing how singularities in data relate and determining visibility conditions, supported by numerical experiments.

## Contribution

It demonstrates that the measurement operator is a Fourier Integral Operator and characterizes the visibility of singularities in variable wave speed scenarios.

## Key findings

- Measurement operator is a Fourier Integral Operator.
- Visibility of singularities depends on the canonical relation.
- Numerical results validate theoretical analysis.

## Abstract

We explore Thermoacoustic Tomography with circular integrating detectors assuming variable, smooth wave speed. We show that the measurement operator in this case is a Fourier Integral Operator and examine how the singularities in initial data and measured data are related through the canonical relation of this operator. We prove which of those singularities in the initial data are visible from a fixed open subset of the set on which measurements are taken. In addition, numerical results are shown for both full and partial data.