Point Spread Function Estimation in X-Ray Imaging with Partially Collapsed Gibbs Sampling

Abstract

The point spread function (PSF) of a translation invariant imaging system is its impulse response, which cannot always be measured directly. This is the case in high-energy X-ray radiography, and the PSF must be estimated from images of calibration objects indirectly related to the impulse response. When the PSF is assumed to have radial symmetry, it can be estimated from an image of an opaque straight edge. We use a nonparametric Bayesian approach, where the prior probability density for the PSF is modeled as a Gaussian Markov random field and radial symmetry is incorporated in a novel way. Markov chain Monte Carlo posterior estimation is carried out by adapting a recently developed improvement to the Gibbs sampling algorithm, referred to as partially collapsed Gibbs sampling. Moreover, the algorithm we present is proven to satisfy invariance with respect to the target density. Finally, we demonstrate the efficacy of these methods on radiographic data obtained from a high-energy X-ray diagnostic system at the U. S. Department of Energy's Nevada National Security Site.