Exact inversion of the conical Radon transform with a fixed opening angle

Abstract

We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In ${\mathbb{R}}^3$ it maps a function to its surface integrals over circular cones, and in ${\mathbb{R}}^2$ it maps a function to its integrals along two rays with a common vertex. Such transforms appear in various mathematical models arising in medical imaging, nuclear industry and homeland security. This paper contains new results about inversion of conical Radon transform with fixed opening angle and vertical central axis in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$. New simple explicit inversion formulae are presented in these cases. Numerical simulations were performed to demonstrate the efficiency of the suggested algorithm in 2D.

13 pages

References in corpus (3)

• Single-Scattering Optical Tomography
• Inversion formulas for the broken-ray Radon transform
• Broken ray tomography in the disk

Cited by in corpus (6)

• Inversion of the star transform
• Generalized V-line transforms in 2D vector tomography
• Variational regularization of the weighted conical Radon transform
• Recovery of singularities for the weighted cone transform appearing in the Compton camera imaging
• The Broken Ray Transform: Additional Properties and New Inversion Formula
• Second-Harmonic Imaging in Random Media