Sampling-based uncertainty quantification in deconvolution of X-ray radiographs

Abstract

In imaging applications that focus on quantitative analysis–such as X-ray radiography in the security sciences–it is necessary to be able to reliably estimate the uncertainties in the processing algorithms applied to the image data, and deconvolving the system blur out of the image is usually an essential step. In this work we solve the deconvolution problem within a Bayesian framework for edge-enhancing reconstruction with uncertainty quantification. The likelihood is a normal approximation to the Poisson likelihood, and the prior is generated from a classical total variation regularized Poisson deconvolution. Samples from the corresponding posterior distribution are computed using a Markov chain Monte Carlo approach, giving a pointwise measure of uncertainty in the reconstructed signal. We demonstrate the results on real data used to calibrate a high-energy X-ray source and show that this approach gives reconstructions as good as classical regularization methods, while mitigating many of their drawbacks.