Resolving Variable Respiratory Motion From Unsorted 4D Computed Tomography

4D Computed Tomography (4DCT) is widely used for many clinical applications such as radiotherapy treatment planning, PET and ventilation imaging. However, common 4DCT methods reconstruct multiple breath cycles into a single, arbitrary breath cycle which can lead to various artefacts, impacting the downstream clinical applications. Surrogate driven motion models can estimate continuous variable motion across multiple cycles based on CT segments `unsorted' from 4DCT, but it requires respiration surrogate signals with strong correlation to the internal motion, which are not always available. The method proposed in this study eliminates such dependency by adapting the hyper-gradient method to the optimization of surrogate signals as hyper-parameters, while achieving better or comparable performance, as demonstrated on digital phantom simulations and real patient data. Our method produces a high-quality motion-compensated image together with estimates of the motion, including breath-to-breath variability, throughout the image acquisition. Our method has the potential to improve downstream clinical applications, and also enables retrospective analysis of open access 4DCT dataset where no respiration signals are stored. Code is avaibale at https://github.com/Yuliang-Huang/4DCT-irregular-motion.