  Computed tomography (CT) equivalent information is needed for attenuation
correction in PET imaging and for dose planning in radiotherapy. Prior work has
shown that Gaussian mixture models can be used to generate a substitute CT
(s-CT) image from a specific set of MRI modalities. This work introduces a more
flexible class of mixture models for s-CT generation, that incorporates spatial
dependency in the data through a Markov random field prior on the latent field
of class memberships associated with a mixture model. Furthermore, the mixture
distributions are extended from Gaussian to normal inverse Gaussian (NIG),
allowing heavier tails and skewness. The amount of data needed to train a model
for s-CT generation is of the order of 100 million voxels. The computational
efficiency of the parameter estimation and prediction methods are hence
paramount, especially when spatial dependency is included in the models. A
stochastic Expectation Maximization (EM) gradient algorithm is proposed in
order to tackle this challenge. The advantages of the spatial model and NIG
distributions are evaluated with a cross-validation study based on data from 14
patients. The study show that the proposed model enhances the predictive
quality of the s-CT images by reducing the mean absolute error with 17.9%.
Also, the distribution of CT values conditioned on the MR images are better
explained by the proposed model as evaluated using continuous ranked
probability scores.
