MCMC for High Energy X-Ray Radiography
Image deblurring via deconvolution can be formulated as a hierarchical Bayesian inverse problem, and numerically solved by Markov Chain Monte Carlo (MCMC) methods. Numerical solution is difficult because inconsistent assumptions about the data outside of the field of view of the image lead to artifacts near the boundary; and the Bayesian inverse problem is high-dimensional for high-resolution images. The numerical MCMC framework I present addresses these issues. Boundary artifacts are reduced by reconstructing the image outside the field of view. Numerical difficulties that arise from high-dimensions are mitigated by exploiting sparse problem structure in the prior precision matrix.