Convexity for the diffuse tomography model

The diffuse tomography model consists of a discrete model for the migration of particles inside a medium whereby such particles move according to a two-step Markov process. The underlying variables that determine the medium at a given pixel are the particle survival probability and the turning probabilities. The latter depend on the angle between the incoming and outgoing directions. The external measurements predicted by this model turn out to be highly nonlinear functions of the medium parameters. This makes the inverse problem associated with this model very complex and computer intensive. We show that after a suitable change of variables the external measurements for the diffuse tomography model become convex functions defined on a convex domain. We also discuss some of the algorithmic implications of such a convexity result in designing efficient solution methods for the inverse problem.