Al Scott Prize Lecture: Scalable block Gibbs sampling for image deblurring in X-ray radiography
In quantitative X-ray radiography, blur in radiographic images can be modeled as a convolution with additive noise. One means of reducing and quantifying the noise and blur in these images is to solve the associated inverse problem, deconvolution, within a Bayesian framework. Markov chain Monte Carlo (MCMC) methods are often used to sample from the posterior distribution in Bayesian modeling, but often perform poorly as the size of the image increases, both in terms of computational tractability and convergence of the Markov chain. In this work, we exploit the structure of deconvolution with sparse regularization and the local nature of the problem in order to develop a scalable block Gibbs sampler for large-scale image deblurring with data-driven boundary conditions. Results are presented on experimental images of size 4096 by 4096 pixels from the U.S. Department of Energy's Nevada National Security Site, and the performance of the MCMC scheme is characterized by the integrated autocorrelation time of the Markov chain and the computational cost per sample.