On the determination of a function from cylindrical Radon transforms

TL;DR

This paper investigates a Radon-type transform in Photoacoustic Tomography with line detectors, providing Fourier slice theorems, inversion formulas, support theorems, stability estimates, and range conditions for cylindrical and planar detector configurations.

Contribution

It introduces new inversion formulas and theoretical results for Radon transforms with line detectors in cylindrical and planar geometries, advancing image reconstruction methods in Photoacoustic Tomography.

Findings

Fourier slice theorems established for both detector configurations

New inversion formulas derived for the Radon-type transforms

Support, stability, and range conditions characterized

Abstract

This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent to the boundary of a cylindrical domain and when the line detectors are located on a plane. We present the analogue of the Fourier slice theorems for each case of the Radon-type transforms. Also, we provide several new inversion formulas, a support theorem, and stability estimate and necessary range condition results.