A Bayesian approach to CT reconstruction with uncertain geometry. Issue 1 (31st December 2023)

• Record Type: Journal Article
• Authors: Pedersen, Frederik Hagsholm; Jørgensen, Jakob Sauer; Andersen, Martin Skovgaard
• Is Part Of: Applied mathematics in science and engineering. Volume 31:Issue 1(2023)
• Publication Date: 2023-12-31
• Subjects: Computed tomography -- model errors -- reconstruction methods -- parameter estimation -- uncertainty quantification; 62F15 -- 60J22 -- 65F22 -- 15A29 -- 65C20; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2023.2166041
• Languages: English
• ISSNs: 2769-0911

Abstract

ABSTRACT: Computed tomography (CT) is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for CT are based on the assumption that the projection geometry, which describes the relative location and orientation of the radiation source, object, and detector for each projection, is exactly known. However, in practice, these geometric parameters 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 center-of-rotation offset for fan-beam tomography. The reconstruction method is based on a Bayesian approach that yields a point estimate for the reconstruction and center-of-rotation offset and, in addition, provides valuable information regarding their uncertainty. This is achieved by approximately sampling from the joint posterior distribution of the reconstruction and center-of-rotation offset using a hierarchical Gibbs sampler. Our methodology is highly flexible and can be adapted to other geometric parameters and/or scan modes. Through numerical experiments based on real tomographic data, we compare the proposed Bayesian method to two existing approaches to the problem of correcting the geometry and demonstrate that our method achieves comparable or better results under challenging conditions.