  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 it 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 non-parametric 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.
