Analytic and accurate reconstruction method for x-ray dark-field computed tomography

The x-ray dark-field imaging provides enhanced sensitivity to alveolar structure compared to conventional x-ray imaging and has the potential of clinical application for lung disease diagnosis. Up to now, a human-scale dark-field computed tomography (CT) prototype has been developed. One challenge in the dark-field CT is the positional dependence of the dark-field signal. The signal is rotation variant during a CT scan, making conventional reconstruction methods imprecise. To address this issue, the dark-field CT is modeled as a weighted Radon transform in this work. By applying the analytical inversion formula to this model, dark-field images can be reconstructed without artefacts caused by the positional dependence. This method has been validated through simulated and experimental data.