Fully Bayesian Reconstructions from Single-Photon Emission Computed Tomography Data

Abstract

With suitably chosen priors, Bayesian models are useful in image reconstruction. I consider reconstructions from single-photon emission computerized tomography data using a Gibbs pairwise difference prior. A fully Bayesian approach is presented where the prior parameters are considered drawn from hyperpriors. The approach is problematical, because the normalization constant in the prior is an intractable function of its parameters. Here the constant is estimated off-line by reverse logistic regression. Markov chain Monte Carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds. The resulting reconstructions are compared to those obtained by filtered back-projection, maximum likelihood/EM, and the one-step-late solution to the fixed parameter posterior mode.

Key Words:

• Fully Bayesian
• Gibbs prior
• Hastings algorithm
• Markov chain Monte Carlo
• Normalizing constant
• Reverse logistic regression
• Single-photon emission computerized tomography