Abstract:
At least since the seminal work of Geman and Geman {1984), Markov random fields have served as Bayesian models for images in computational reconstruction from degraded, observational data. We consider fully Bayesian hierarchical models, in which one stage of the hierarchy is a Markov random field. This field is parameterized by a scalar lambda which in principle controls the degree of smoothness of random images generated by the model. We then develop a class of conjugate priors for lambda. Based on data, posterior inferences are developed employing familiar versions of Gibbs' Sampling. The basic hierarchical model is extended to an exchangeable model in which several "similiar" images are to be reconstructed. Artificial examples, motivated by imaging problems arising in materials science and stereology, are presented.
Keywords:
Bayesian analysis; Conjugate priors; Exchangeability; Gibbs sampling.
tr15.pdf