Range Description of a Conical Radon Transform

TL;DR

This paper characterizes the range of the Conical Radon Transform, which integrates functions over circular cones, with implications for imaging techniques like Compton camera and optical tomography.

Contribution

It provides a new range description for the Conical Radon Transform depending on the dimension's parity, advancing understanding of its mathematical properties.

Findings

Range description varies with the parity of n

Results apply to Compton camera imaging models

Enhances mathematical understanding of cone-based transforms

Abstract

In this work we consider the Conical Radon Transform, which integrates a function on $\R^n$ over families of circular cones. Transforms of this type are known to arise naturally as models of Compton camera imaging and single-scattering optical tomography (in the latter case, when $n=2$). The main results (which depend on the parity of $n$) provide a description of the range of the transform on the space $C_0^\infty(\R^n)$