**Abstract:** The last two decades have seen a paradigm shift in inverse problems, from computing single, approximately optimal answers to generating distributions of solutions that are used to quantify the associated uncertainties. To this end, Bayesian models, with Markov Chain Monte Carlo or other sampling schemes, have become standard, and, in this work, we will present hierarchical Bayesian formulations for linear inverse problems in X-ray imaging. Different desired features in data reconstructions require different assumptions on the data – and therefore different priors – and we will show an approach that allows one to “sample” the precision matrix associated with the prior. This results in image reconstructions that can incorporate smoothness or total-variation type assumptions into a single scheme, while relaxing the assumption that an entire image is smooth everywhere or is entirely piecewise constant. The purpose of hierarchical models is to relax the sensitivity of the reconstruction on the choices of scale (regularization) parameters, and we will conclude with recent work characterizing the robustness of hierarchical reconstructions and the challenges in using hierarchical models for uncertainty quantification.

# 'Hierarchical Bayesian Models for X-ray Imaging: Computational Considerations for Uncertainty Quantification in Inverse Problems'

6 April 2018

12:00 pm to 1:00 pm

'Hierarchical Bayesian Models for X-ray Imaging: Computational Considerations for Uncertainty Quantification in Inverse Problems'

Marylesa Howard and Aaron Luttman

Nevada National Security Site