# Operator learning approach for the limited view problem in photoacoustic tomography

## TL;DR

This paper introduces an operator learning method to extend limited boundary measurements in photoacoustic tomography, improving image reconstruction by reducing artifacts caused by incomplete data.

## Contribution

It proposes a novel operator learning approach to approximate boundary data extension, enhancing reconstruction quality in limited view photoacoustic tomography.

## Key findings

- The approach effectively reduces reconstruction artifacts.
- Numerical results support the theoretical error analysis.
- The method improves image quality with limited boundary data.

## Abstract

In photoacoustic tomography, one is interested to recover the initial pressure distribution inside a tissue from the corresponding measurements of the induced acoustic wave on the boundary of a region enclosing the tissue. In the limited view problem, the wave boundary measurements are given on the part of the boundary, whereas in the full view problem, the measurements are known on the whole boundary. For the full view problem, there exist various fast and robust reconstruction methods. These methods give severe reconstruction artifacts when they are applied directly to the limited view data. One approach for reducing such artefacts is trying to extend the limited view data to the whole region boundary, and then use existing reconstruction methods for the full view data. In this paper, we propose an operator learning approach for constructing an operator that gives an approximate extension of the limited view data. We consider the behavior of a reconstruction formula on the extended limited view data that is given by our proposed approach. Approximation errors of our approach are analyzed. We also present numerical results with the proposed extension approach supporting our theoretical analysis.