Range Description of a Conical Radon Transform

Abstract

In this work we consider the Conical Radon Transform, which integrates a function on ${\mathbb{R}}^n$ 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 $C_0^{\infty }({\mathbb{R}}^n)$

32 pages, 11 figures, revision

References in corpus (2)

• Detecting small low emission radiating sources
• On the determination of a function from its cone transform with fixed central axis