  In this paper we demonstrate the utility of fusing energy-resolved
observations of Compton scattered photons with traditional attenuation data for
the joint recovery of mass density and photoelectric absorption in the context
of limited view tomographic imaging applications. We begin with the development
of a physical and associated numerical model for the Compton scatter process.
Using this model, we propose a variational approach recovering these two
material properties. In addition to the typical data-fidelity terms, the
optimization functional includes regularization for both the mass density and
photoelectric coefficients. We consider a novel edge-preserving method in the
case of mass density. To aid in the recovery of the photoelectric information,
we draw on our recent method in \cite{r15} and employ a non-local
regularization scheme that builds on the fact that mass density is more stably
imaged. Simulation results demonstrate clear advantages associated with the use
of both scattered photon data and energy resolved information in mapping the
two material properties of interest. Specifically, comparing images obtained
using only conventional attenuation data with those where we employ only
Compton scatter photons and images formed from the combination of the two,
shows that taking advantage of both types of data for reconstruction provides
far more accurate results.
