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

The authors study the relationship between the choice of parameters for a generalized Gibbs prior for the maximum a posteriori, expectation maximization (MAP-EM) algorithm, and the model of the projection/backpropagation process used in single photon emission tomography (SPECT) reconstruction. 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 compensation, 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, it is concluded that, for each projection model, there is an optimal value of the weighting parameter which decreases as the projection process is modeled more accurately