Techniques for regularization parameter and hyper-parameter selection in PET and SPECT imaging

Penalized maximum likelihood methods are commonly used in positron emission tomography (PET) and single photon emission computed tomography (SPECT). Due to the fact that a Poisson data-noise model is typically assumed, standard regularization parameter choice methods, such as the discrepancy principle or generalized cross validation, cannot be directly applied. In the recent work of the authors, regularization parameter choice methods for penalized negative-log Poisson likelihood problems are introduced. In this article, we apply these methods to the applications of PET and SPECT, introducing a modification that improves the performance of the methods. We then demonstrate how these techniques can be used to choose the hyper-parameters in a Bayesian hierarchical regularization approach.