Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography (Communications in Computational Physics, 2020)
High-energy X-ray radiography is a measuring technique for quantitativemeasurement and diagnosis of the object and its internal structure. Tomographic reconstruction determines the geometric and physical properties of the object accordingto the energy distribution on the imaging plane. Considering the noise and blur in theprocess of radiographing, we construct a general reconstruction model for the axisymmetric single image photographic system. This inverse problem is then cast within astatistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesianmodel is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown nonnegative density profile, the precision matrix, and twoscale parameters. This results in a joint posterior distribution, which can be readilysampled using the Markov chain Monte Carlo (MCMC) method. To study the role ofhyperparameters and their sensitivity analysis, a wide variety of tests were conductedwhich led to a number of definitive conclusions. Results of the density reconstructionsand pointwise uncertainty estimates are presented for simulated signals with variousphysical factors in the imaging process included.
Keywords: Inverse problem; density reconstruction; uncertainty quantification; Bayesian inference; MCMC method.