  Characterizing statistical properties of solutions of inverse problems is
essential for decision making. Bayesian inversion offers a tractable framework
for this purpose, but current approaches are computationally unfeasible for
most realistic imaging applications in the clinic. We introduce two novel deep
learning based methods for solving large-scale inverse problems using Bayesian
inversion: a sampling based method using a WGAN with a novel mini-discriminator
and a direct approach that trains a neural network using a novel loss function.
The performance of both methods is demonstrated on image reconstruction in
ultra low dose 3D helical CT. We compute the posterior mean and standard
deviation of the 3D images followed by a hypothesis test to assess whether a
"dark spot" in the liver of a cancer stricken patient is present. Both methods
are computationally efficient and our evaluation shows very promising
performance that clearly supports the claim that Bayesian inversion is usable
for 3D imaging in time critical applications.
