Spectrally Focused Markov Random Field Image Modeling in 3D CT

Markov random fields (MRFs) are a broadly useful and relatively economical stochastic model for imagery in Bayesian estimation. The simplicity of their most common examples allows local computation in iterative optimization, and statistical descriptions of image ensembles which discourage dramatic behavior, particularly under models with strictly convex potential functions. This simplicity may be a liability, however, when the inherent bias of minimum mean-squared error or maximum a posteriori probability (MAP) estimators attenuate all but the lowest spatial frequencies. For applications where more flexibility in spectral response is desired, potential benefit exists in models which accord higher a priori probabilities to content in higher frequencies. This paper illustrates the gains possible with MRF design similar to inner bone emphasis in conventional X-ray CT reconstruction.