# Photoacoustic Tomography with Direction Dependent Data: An Exact Series Reconstruction Approach

## TL;DR

This paper develops exact series reconstruction formulas for photoacoustic tomography with direction-dependent data, accounting for detectors with directivity and frequency dependence, and demonstrates their robustness through numerical results.

## Contribution

It introduces a novel exact frequency domain reconstruction method for data combining acoustic pressure and its normal derivative, specifically for spherical detection geometries.

## Key findings

- Reconstruction formulas are robust and accurate.
- Measurement model significantly influences the recovered initial pressure.
- Numerical results validate the theoretical formulas.

## Abstract

Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the measured data are more accurately described as a linear combination of the acoustic pressure and its normal derivative on the detection surface. In this paper, we consider the inverse source problem for data that are a combination of an acoustic pressure of the wave equation and its normal derivative For the special case of a spherical detection geometry we derive exact frequency domain reconstruction formulas. We present numerical results showing the robustness and validity of the derived formulas. Moreover, we compare several different combinations of the pressure and its normal derivative showing that used measurement model significantly affects the recovered initial pressure.