Statistical modelling of the chest radiograph and simulation in a Bayesian framework

The authors have recently developed a new statistical model for chest X-ray image formation. Here, they utilise Bayesian sampling to study the characteristics of the distributions of the random variables in this model. Using the Metropolis-Hastings algorithm on a clinically acquired image, posterior samples were generated from the distribution of mean direct detected photons (ideal image). From these samples, posterior (marginal) distributions could be found, and these proved to be unimodal, indicating that point estimation schemes such as GEM methods are likely to be close to optimal. It could also be seen that the sampling (conditional) distributions favor a wide range of exposure values for chest X-ray data. The sampling correlation proved to be on the order of 100 iterations, indicating that the chances of successfully using sampling algorithms such as Markov Chain Monte Carlo to do or evaluate image estimation is high. The general framework described can also be used for validation of approximations made in the derivation of the model.