Automated Estimation of the Parameters of Gibbs Priors to be Used in Binary Tomography

Abstract

Image modeling using Gibbs priors was shown to be effective in image reconstruction problems. This motivated us to evaluate three techniques for estimating the priors: the heuristic method, the histogram method and Borges' method. We found that both the histogram and Borges' method accurately recovered the parameters needed to specify four different Gibbs distributions from training sets consisting of random sample images from those distributions. This was not the case for the heuristic method. We evaluated the usefulness of the estimated distributions as priors for binary tomography in two experiments: in one the images for the training set were taken from a Gibbs distribution determined by five parameters, and they were typical cardiac phantom images for the second one. We estimated the parameters using both the heuristic and Borges' method in both experiments. We used a modified Metropolis algorithm for the reconstructions. In the first experiment both estimation methods gave rise to excellent reconstructions, but this was not the case for the second experiment; however, even in this case typically less than four percent of the pixels were mis-classified in the reconstructions.