  Positron emission tomography (PET) is an important functional medical imaging
technique often used in the evaluation of certain brain disorders, whose
reconstruction problem is ill-posed. The vast majority of reconstruction
methods in PET imaging, both iterative and deep learning, return a single
estimate without quantifying the associated uncertainty. Due to ill-posedness
and noise, a single solution can be misleading or inaccurate. Thus, providing a
measure of uncertainty in PET image reconstruction can help medical
practitioners in making critical decisions. This paper proposes a deep
learning-based method for uncertainty quantification in PET image
reconstruction via posterior sampling. The method is based on training a
conditional generative adversarial network whose generator approximates
sampling from the posterior in Bayesian inversion. The generator is conditioned
on reconstruction from a low-dose PET scan obtained by a conventional
reconstruction method and a high-quality magnetic resonance image and learned
to estimate a corresponding standard-dose PET scan reconstruction. We show that
the proposed model generates high-quality posterior samples and yields
physically-meaningful uncertainty estimates.
