Uncertainty assessment for reconstructions based on deformable models

Deformable geometric models can be used in the context of Bayesian analysis to solve ill-posed tomographic reconstruction problems. The uncertainties associated with a Bayesian analysis may be assessed by generating a set of random samples from the posterior, which may be accomplished using a Markov-Chain Monte-Carlo (MCMC) technique. We demonstrate the combination of these techniques for a reconstruction of a two-dimensional object from two orthogonal noisy projections. The reconstructed object is modeled in terms of a deformable geometrically-defined boundary with a uniform interior density yielding a nonlinear reconstruction problem. We show how an MCMC sequence can be used to estimate uncertainties in the location of the edge of the reconstructed object.