A Radon-type transform arising in Photoacoustic Tomography with circular detectors: spherical geometry

TL;DR

This paper introduces a Radon-type transform in Photoacoustic Tomography with circular detectors, decomposes it into known transforms, and develops an inversion method validated by numerical simulations.

Contribution

It presents a novel Radon-type transform specific to circular detector configurations and derives an inversion formula by combining existing transform techniques.

Findings

Transform can be decomposed into spherical Radon and Funk-Minkowski transforms.

Inversion formula successfully reconstructs images in simulated experiments.

Numerical simulations demonstrate the effectiveness of the proposed algorithm.

Abstract

This paper is devoted to a Radon-type transform arising in a version of Photoacoustic Tomography that uses integrating circular detectors. We show that the transform can be decomposed into the spherical Radon transform and the Funk-Minkowski transform. An inversion formula and a range description are obtained by combining existing inversion for- mulas and range descriptions for the spherical Radon transform and the Funk-Minkowski transform. Numerical simulations are performed to demonstrate our proposed algorithm.