Deep posterior sampling: Uncertainty quantification for large scale inverse problems

Jonas Adler, Ozan Öktem

Keywords: GAN, Inverse Problem, CT, Image Reconstruction, Bayesian Inversion

TL;DR: Use WGAN to sample from the posterior in CT image reconstruction

Abstract:

The goal in an inverse problem is to recover a hidden model parameter from noisy indirect observations. Such problems arise in several areas of science and industry and their solutions form the basis for decision making, like when imaging is used in medicine.
Inverse problems are often ill-posed, meaning that there can be multiple solutions consistent with observations and small errors in data result in large errors in the solution. Hence, it is important to assess the uncertainty in the solution of an ill-posed problem and especially so when critical decisions are based on the solution. Bayesian inversion offers a coherent framework for both solving an ill-posed inverse problem and quantifying the uncertainty in its solution. Its applicability is however limited by the ability to select a sufficiently `good' prior and capability to manage the computational burden.
We show how a conditional WGAN with a novel minibatch discriminator can be used to sample from the posterior in Bayesian inversion. The suggested approach is demonstrated for image-guided medical diagnostics using computed tomography.

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