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.