Estimating Uncertainty in PET Image Reconstruction via Deep Posterior
  Sampling
Tin Vlašić Tomislav Matulić Damir Seršić
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.