Contributed Talk: Deep Bayesian Inversion

Abstract

The ability to better characterize statistical properties of solutions to many inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for such an analysis, but current approaches are computationally unfeasible for most realistic imaging applications in the clinic and asymptotic characterizations rely on unrealistic assumptions. We show how deep learning can be used for Bayesian inversion by introducing two novel methods: a sampling based method using GANs and a direct approach that trains a neural network using a novel loss function. We demonstrate the capabilities of both methods by performing uncertainty quantification on ultra low dose 3D helical CT. We estimate the posterior mean and standard deviation of the 3D images and furthermore perform a Bayesian hypothesis test to assess the presence of a ‘dark spot’ in the liver of a cancer stricken patient.