Summary: 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 recent work of the authors [see SIAM J. Sci. Comput. 32, No. 1, 171–185 (2010; Zbl 1215.65116
); ibid. 25, No. 4, 1326–1343 (2003; Zbl 1061.65047
)] , regularization parameter choice methods for penalized negative-log Poisson likelihood problems are introduced. 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.