Analytical Reconstruction of Human-Scale Dark-Field CT

Grating-based X-ray dark-field imaging leverages the small-angle scattering from porous structures, providing enhanced sensitivity to alveoli in lung parenchyma. It shows the potential of clinical application for lung disease diagnosis, and has been implemented in human-scale dark-field computed tomography (CT). One challenge in the dark-field CT is the positional dependence of the dark-field signal, which varies with rotation during a CT scan. This rotational variance limits the accuracy of conventional reconstruction methods, particularly in large field-of-view as for humans. While calibration methods have been proposed to address this issue, they are either computationally intensive or impose constraints on the scanning trajectory. In this work, we model the dark-field CT as a weighted Radon transform. By applying the analytical inversion formula to this model, we achieve the dark-field CT reconstruction without artefacts from positional dependence. This approach eliminates the requirement for conjugate ray pairs, allowing extensions from fan-beam to cone-beam geometry through coordinate transform. Simulations and experiments were conducted to validate this method using an anthropomorphic chest phantom.