BAYESIAN IMAGE-RECONSTRUCTION IN SPECT USING HIGHER-ORDER MECHANICAL MODELS AS PRIORS

While the ML-EM algorithm for reconstruction for emission tomography i s unstable due to the ill-posed nature of the problem. Bayesian recons truction methods overcome this instability by introducing prior inform ation, often in the form of a spatial smoothness regularizer. More ela borate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual sp atial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise consta nt source distribution. Here, we propose an extension to a piecewise l inear model-the weak plate-which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but als o allows for piecewise ramplike regions in the reconstruction. Indeed, for our application in SPECT, such ramplike regions are observed in g round-truth source distributions in the form of primate autoradiograph s of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, we model the prior as a Gibbs distribution and use a GEM for mulation for the optimization. We compare quantitative performance of the ML-EM algorithm, a GEM algorithm with a prior favoring piecewise c onstant regions, and a GEM algorithm with our weak plate prior. Pointw ise and regional bias and variance of ensemble image reconstructions a re used as indications of image quality. Our results show that the wea k plate and membrane priors exhibit improved bias and variance relativ e to ML-EM techniques.