Bayesian Tomographic Reconstruction Using Riemannian MCMC

This paper describes the use of Monte Carlo sampling for tomographic image reconstruction. We describe an efficient sampling strategy, based on the Riemannian Manifold Markov Chain Monte Carlo algorithm, that exploits the peculiar structure of tomographic data, enabling efficient sampling of the high-dimensional probability densities that arise in tomographic imaging. Experiments with positron emission tomography (PET) show that the method enables the quantification of the uncertainty associated with tomographic acquisitions and allows the use of arbitrary risk functions in the reconstruction process.