Penalized maximum likelihood methods are commonly used in positron emission tomography (PET). 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, can not be directly applied. In recent work of the authors, regularization parameter choice methods for penalized negative-log Poisson likelihood problems are introduced, and the application is image deconvolution. In this paper, we extend those methods to the application of PET, introducing a minor modification that seems to improve the performance of the methods. Moreover, we show how these methods can be used to choose the hyper-parameters in a Bayesian hierarchical regularization approach, also of the authors' previous work.

Keywords: positron emission tomography, inverse problems, regularization parameter selection, Bayesian statistical methods, Poisson noise