  Here we present new joint reconstruction and regularization techniques
inspired by ideas in microlocal analysis and lambda tomography, for the
simultaneous reconstruction of the attenuation coefficient and electron density
from X-ray transmission (i.e., X-ray CT) and backscattered data (assumed to be
primarily Compton scattered). To demonstrate our theory and reconstruction
methods, we consider the "parallel line segment" acquisition geometry of Webber
and Miller ("Compton scattering tomography in translational geometries."
Inverse Problems 36, no. 2 (2020): 025007), which is motivated by system
architectures currently under development for airport security screening. We
first present a novel microlocal analysis of the parallel line geometry which
explains the nature of image artefacts when the attenuation coefficient and
electron density are reconstructed separately. We next introduce a new joint
reconstruction scheme for low effective $Z$ (atomic number) imaging ($Z<20$)
characterized by a regularization strategy whose structure is derived from
lambda tomography principles and motivated directly by the microlocal analytic
results. Finally we show the effectiveness of our method in combating noise and
image artefacts on simulated phantoms.
