Exact Series Reconstruction in Photoacoustic Tomography with Circular Integrating Detectors

TL;DR

This paper introduces an exact reconstruction method for 3D photoacoustic tomography using circular integrals, involving inversion formulas for an inverse wave problem and validated by numerical results.

Contribution

It provides new inversion formulas for reconstructing images from circular integral data in photoacoustic tomography, addressing an inverse wave equation problem.

Findings

Inversion formulas are derived for the first reconstruction step.

Numerical results demonstrate the method's validity and robustness.

The approach enables exact 3D image reconstruction in photoacoustic tomography.

Abstract

A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of circular integrating are used to reconstruct the circular projection of the source distribution. In the second step the inverse circular Radon transform is applied. In this article we establish inversion formulas for the first step, which involves an inverse problem for the axially symmetric wave equation. Numerical results are presented that show the validity and robustness of the resulting algorithm.