Image restoration and reconstruction with a Bayesian approach.

We have extended Johnson's Bayesian method for image restoration and reconstruction by introducing diagonal line sites, using symmetric neighborhood configurations, and employing an additional hyperparameter for estimation of line sites. A general formulation for arbitrary neighborhood configurations was derived. The major part of this paper deals with the conduct of computer simulations intended to examine the effect of the hyperparameters, the diagonal line sites, and the size of the neighborhood configuration on the performance of the proposed Bayesian method. We show that, for optimal performance, distinct hyperparameters should be used for the intensity sites and line sites. The results also suggest that a large neighborhood configuration should be used. By comparing the near-optimal restored images, we demonstrated that the use of diagonal line sites, along with the symmetric configurations thus made possible, can effectively remove the blocky edge artifacts and produce images of better quality. When the method was applied to positron emission tomography (PET) image reconstruction, our results showed that the quality of the reconstructed images was improved for both computer-simulated and real patient PET data.