New Loss Functions in Bayesian Imaging

Abstract

Unlike the development of more accurate prior distributions for use in Bayesian imaging, the design of more sensible estimators through loss functions has been neglected in the literature. We discuss the design of loss functions with a local structure that depend only on a binary misclassification vector. The proposed approach is similar to modeling with a Markov random field. The Bayes estimate is calculated in a two-step algorithm using Markov chain Monte Carlo and simulated annealing algorithms. We present simulation experiments with the Ising model, where the observations are corrupted with Gaussian and flip noise.

Key Words:

• Bayesian inference
• Image reconstruction
• Image restoration
• Markov random field