Range Description of a Conical Radon Transform

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 $C_0^\infty(\R^n)$