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.

[1]  HighWire Press.  Philosophical Transactions of the Royal Society of London , 1781, The London Medical Journal.

[2]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[3]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[4]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  L. Shepp,et al.  A Statistical Model for Positron Emission Tomography , 1985 .

[6]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[7]  Stuart Geman,et al.  Statistical methods for tomographic image reconstruction , 1987 .

[8]  Linda Kaufman,et al.  Implementing and Accelerating the EM Algorithm for Positron Emission Tomography , 1987, IEEE Transactions on Medical Imaging.

[9]  S. Webb.  The Physics of Medical Imaging , 1990 .

[10]  P. Green.  Bayesian reconstructions from emission tomography data using a modified EM algorithm. , 1990, IEEE transactions on medical imaging.

[11]  P. Green,et al.  Global and local priors, and the location of lesions using gamma-camera imagery , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[12]  Jorge Núñez de Murga,et al.  Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies , 1993, IEEE Trans. Medical Imaging.

[13]  C. Geyer.  Estimating Normalizing Constants and Reweighting Mixtures , 1994 .

[14]  P. Green,et al.  Modelling data from single photon emission computed tomography , 1994 .

[15]  Kerrie Mengersen,et al.  [Bayesian Computation and Stochastic Systems]: Rejoinder , 1995 .

[16]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[17]  C. Geyer,et al.  Annealing Markov chain Monte Carlo with applications to ancestral inference , 1995 .

[18]  Peter J Green,et al.  Markov chain Monte Carlo in image analysis , 1996 .

[19]  Ronald J. Jaszczak,et al.  Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data , 1997, IEEE Transactions on Medical Imaging.

[20]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[21]  A. Sokal.  Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms , 1997 .