An Inversion Formula for Horizontal Conical Radon Transform

TL;DR

This paper derives an explicit inversion formula for the horizontal conical Radon transform, utilizing the vertical slice transform on a sphere and the V-line transform on a plane, advancing mathematical tomography techniques.

Contribution

The paper introduces a novel explicit inversion formula for the horizontal conical Radon transform, connecting it with existing transforms on spheres and planes.

Findings

Derived an explicit inversion formula for the transform.

Connected the inversion with vertical slice and V-line transforms.

Provides a new mathematical tool for tomography applications.

Abstract

In this paper, we consider the conical Radon transform on all cones with horizontal central axis whose vertices are on a straight line. We derive an explicit inversion formula for such transform. The inversion makes use of the vertical slice transform on a sphere and V-line transform on a plane.