  Computed tomography is a method for synthesizing volumetric or
cross-sectional images of an object from a collection of projections. Popular
reconstruction methods for computed tomography are based on idealized models
and assumptions that may not be valid in practice. One such assumption is that
the exact projection geometry is known. The projection geometry describes the
relative location of the radiation source, object, and detector for each
projection. However, in practice, the geometric parameters used to describe the
position and orientation of the radiation source, object, and detector are
estimated quantities with uncertainty. A failure to accurately estimate the
geometry may lead to reconstructions with severe misalignment artifacts that
significantly decrease their scientific or diagnostic value. We propose a novel
reconstruction method that jointly estimates the reconstruction and the
projection geometry. The reconstruction method is based on a Bayesian approach
that yields a point estimate for the reconstruction and geometric parameters
and, in addition, provides valuable information regarding their uncertainty.
This is achieved by approximately sampling from the joint posterior
distribution of the reconstruction and projection geometry using a hierarchical
Gibbs sampler. Using real tomographic data, we demonstrate that the proposed
reconstruction method significantly reduces misalignment artifacts. Compared
with two commonly used alignment methods, our proposed method achieves
comparable or better results under challenging conditions.

Numerical Analysis;Numerical Analysis;Applications