Validation of new Gibbs priors for Bayesian tomographic reconstruction using physically acquired data

The variety of Bayesian MAP approaches to tomography proposed in recent years can both stabilize reconstructions and lead to improved bias and variance. In the authors' previous work (see S.J. Lee et al., IEEE Trans. Med. Imaging, vol. MI-14, no. 4, p. 669-80, 1995; S.J. Lee et al., IEEE Trans. Nucl. Sci., vol. NS-44, no. 3, p. 1381-7, 1997), they showed that the thin-plate (TP) prior, which is less sensitive to variations in first spatial derivatives than the conventional membrane (MM) prior, yields improved reconstructions in the sense of low bias. In spite of the several advantages of such quadratic smoothing priors, they are still less than ideal due to their limitations in edge preservation. Here, the authors use a convex-nonquadratic potential function, which provides a degree of edge preservation. As in the case of quadratic priors, a class of two-dimensional smoothing splines with first and second partial derivatives are applied to the new potential function. In order to reduce difficulties such as oversmoothing for MM and edge overshooting for TP, the authors also generalize the prior energy definition to that of a linear combination of MM and TP using a control parameter, and observe its transition between the two extreme cases. To observe the efficacies of their new priors, the authors use physically acquired PET emission data. They also test these priors in a transmission setting with physically acquired transmission data. The authors' results indicate significant improvements in the quality of both emission and transmission images using their new priors.