Some uniqueness theorems for a conical Radon transform

TL;DR

This paper investigates the uniqueness of reconstructing functions from partial data of the conical Radon transform, which is relevant for imaging techniques like astronomy and security involving Compton cameras.

Contribution

It provides new uniqueness theorems for the conical Radon transform with partial domain data, advancing understanding in imaging applications.

Findings

Established conditions for uniqueness with partial data

Extended previous results to more general settings

Implications for imaging techniques using conical Radon data

Abstract

The conical Radon transform, which assigns to a given function $f$ on $\mathbb R^3$ its integrals over conical surfaces, arises in several imaging techniques, e.g. in astronomy and homeland security, especially when the so-called Compton cameras are involved. In many practical situations we know this transform only on a subset of its domain. In these situations, it is a natural question what we can say about $f$ from partial information. In this paper, we investigate some uniqueness theorems regarding a conical Radon transform.