  Here we introduce a new reconstruction technique for two-dimensional Bragg
Scattering Tomography (BST), based on the Radon transform models of [arXiv
preprint, arXiv:2004.10961 (2020)]. Our method uses a combination of ideas from
multibang control and microlocal analysis to construct an objective function
which can regularize the BST artifacts; specifically the boundary artifacts due
to sharp cutoff in sinogram space (as observed in [arXiv preprint,
arXiv:2007.00208 (2020)]), and artifacts arising from approximations made in
constructing the model used for inversion. We then test our algorithm in a
variety of Monte Carlo (MC) simulated examples of practical interest in airport
baggage screening and threat detection. The data used in our studies is
generated with a novel Monte-Carlo code presented here. The model, which is
available from the authors upon request, captures both the Bragg scatter
effects described by BST as well as beam attenuation and Compton scatter.
