A median prior for tomographic reconstruction

We present a convex, edge-preserving prior, which we term a median prior, for regularized (or Bayesian) tomographic reconstruction. With its associated iterative algorithm, the prior can be described approximately as follows: At each iteration k, each object point f_j^k is attracted to the median formed from a local neighborhood surrounding f_j^k, while still trying to satisfy data consistency. With this intuitively appealing approach, it becomes difficult to prove convexity of the objective associated with the prior. However, in this paper, we reformulate the prior so that, while it approximately retains the above behavior, it is provably convex. Anecdotal reconstructions are shown to illustrate the behavior of the new median prior.