Bayesian Image Reconstruction in SPECT Using Higher Order Mechanical Models as Priors

While the ML-EM algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem, Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, we propose an extension to a piecewise linear model -- the weak plate -- which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for our application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radi..