  We study the inversion of the conical Radon which integrates a function in
three-dimensional space from integrals over circular cones. The conical Radon
recently got significant attention due to its relevance in various imaging
applications such as Compton camera imaging and single scattering optical
tomography. The unrestricted conical Radon transform is over-determined because
the manifold of all cones depends on six variables: the center position, the
axis orientation and the opening angle of the cone. In this work, we consider a
particular restricted transform using triple line sensors where integrals over
a three-dimensional set of cones are collected, determined by a one-dimensional
vertex set, a one-dimensional set of central axes, and the one-dimensional set
of opening angle. As the main result in this paper, we derive an analytic
inversion formula for the restricted conical Radon transform. Along that way we
define a certain ray transform adapted to the triple line sensor for which we
establish an analytic inversion formula.
