A generalized Gibbs prior for maximum a posteriori reconstruction in SPECT

In this paper, we introduce a Gibbs prior for use in MAP (maximum a posteriori) reconstruction in SPECT. This new prior, with three parameters, is able to approximate the results of previously-proposed priors with two parameters, as well as a continuum of others. Also, it allows the user increased flexibility in selecting the properties to be emphasized in the final reconstructed image estimate. The additional flexibility offered by the new prior is important in addressing the problem of selecting a prior and its associated parameters in a clinical situation. The paper demonstrates the importance of the derivative potential function (DPF) of the Gibbs distribution in determining which properties will be emphasized in the iterated image estimates. The effects of each of the three parameters are demonstrated on reconstructions from acquired SPECT data. We conclude that the parameters must be chosen carefully with consideration for the object distribution and the relative requirements for low-contrast detail, smoothing and edge sharpness in the reconstructed image.