A Bayesian Approach to CT Reconstruction with Uncertain Geometry

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.