Attenuation and detector response compensations used with gibbs prior distributions for maximum a posteriori SPECT reconstruction

We study the relationship between the choice of parameters for a generalized Gibbs prior for the MAP-EM (Maximum A Posteriori, Expectation Maximization) algorithm, and the model of the projection/backprojection process used in SPECT reconstruction. A realistic phantom, derived from an X-ray CT study and average T1-201 uptake distributions in patients, was used in the investigation. Simulated projection data including nonuniform attenuation, detector response, scatter, and Poisson noise were generated. From this data set, reconstructions were created using a MAP-EM technique with a generalized Gibbs prior, which is designed to smooth noise with minimal smoothing of edge information. The Gibbs prior has three adjustable parameters: one which determines the overall weight placed on the prior in the reconstruction process, and two others which affect the relative smoothing of noise and edges in the reconstructed image estimates. Reconstructions were performed over several different values of the prior parameters for three projector/backprojector models: one with no compensations at all, one incorporating only nonuniform attenuation compensation, and one incorporating both nonuniform attenuation and detector response compensations. Analyzing several measures of image quality in a region-of-interest surrounding the myocardium, we conclude that, for each projection model, there is an optimal value of the weighting parameter which decreases as the projection process is modeled more accurately. We conclude also that the use of the Gibbs prior together with nonuniform attenuation and detector response compensations offers improved quantitative accuracy over Maximum Likelihood EM reconstruction with the same compensations.