Bayesian reconstruction for emission tomography via deterministic annealing

Abstract

In emission tomography, a principled means of incorporating a piecewise smooth prior on the source f is via a mixed variable objective function E(f, 1) defined on f and binary valued line processes 1. MAP estimation on E(f, 1) results in the difficult problem of minimizing an objective function that includes a nonsmooth Gibbs prior ϕ* defined on the spatial derivatives of f. Previous approaches have used heuristic Gibbs potentials ϕ that incorporate line processes, but only approximately. In this work, we present a continuation method in which the correct function ϕ* is approached through a sequence of smooth ϕ functions. Our continuation method is implemented using a GEM-ICM procedure. Simulation results show improvement using our continuation method relative to using ϕ* alone, and to conventional EM reconstructions. Finally, we show a means of generalizing this formalism to the less restrictive case of piecewise linear instead of piecewise fiat priors.