Simulation Evaluation of Gibbs Prior Distributions for use in maximum a Posteriori SPECT Reconstructions

Maximum a posteriori (MAP) reconstruction in SPECT has been shown to have significant advantages over traditional maximum likelihood (ML) methods in terms of noise performance, but these advantages are highly dependent on the choice of the distribution used to model the prior knowledge about the solution image. Several Gibbs prior distributions have been proposed in the literature, but there has been relatively little work comparing and contrasting the effects of these prior distributions on actual reconstructions. We demonstrate the effects of several of these prior distributions in terms of noise characteristics, edge sharpness, and overall quantitative accuracy of the final estimates obtained from an iterative MAP procedure applied to data from a realistic chest phantom. We also examine the effects of the adjustable parameters built into the prior distribution on these properties. We find that these parameter values influence the noise and edge characteristics of the final estimate and can generate reconstructions closer to the actual solution than ML. In addition, we find that the choice of the shape of the prior distribution affects the noise characteristics and edge sharpness in the final estimate.