Regularizing Direct Parametric Reconstruction for Dynamic PET with the Method of Sieves

This paper proposes regularization methods for direct parametric dynamic PET reconstruction, when the space-time activity function needs to be recovered from measurements. In case of high spatial and temporal resolution, the reconstruction is statistically poorly defined, requiring the inclusion of a priori information in the form of a penalty term or filtering. The method of sieves executes filtering in each iteration step, i.e. projects the actual estimate into the subspace of acceptable solutions, and has been successful in reconstructing static data. The objective of this paper is to generalize the filtering scheme for spatio-temporal reconstruction, taking into account that accurate kinetic models describing the temporal behavior are non-linear. Fast changes are impossible to distinguish from noise if only a small temporal window is examined, thus the simple extension to 4D does not provide acceptable results. We show that efficient filtering can be obtained if voxel based model parameters are modified according to the time activity functions of neighboring voxels belonging to the same anatomic region. As the dependence of the time activity function on the model parameters is non-linear for sophisticated kinetic models, the filtering step involves a non-linear parameter fitting, which can be solved analytically for the two-tissue compartment model. The presented method is built into the TeraTomo (TM) system.