Physically interpretable dynamic tomography via a first-principles model

A method for general 4D-computed tomography is introduced via a first-principles consideration of small dynamics partitioned according to the Lagrangian description. The model partitions the dynamics into either kinematics (motion) or non-kinematics under the assumption that the kinematic dynamics are maximal, i.e., kinematics are preferred in any ambiguity of partitioning the dynamics between kinematics and non-kinematics. Alongside dynamic reconstruction, this results in a highly physically interpretable and consistent dynamics model. Parametrisation of the model is achieved via deformation vector fields for the kinematics and sparse arrays named ‘patches’ for the non-kinematics. A method to estimate the dynamics model from a time series of volumes is proposed and employed to analyse a series of phantoms and experimental datasets. Results reveal that the dynamics model can faithfully capture both kinematic and non-kinematic dynamics in both simulated and experimental systems while requiring vastly fewer parameters than a time-series approach. Tomography using this dynamics model is developed via algebraic reconstruction techniques with modified projection operators and projection data. This is tested both with dynamics known a priori and dynamics estimated from projection data via reconstructed volumes. The results show improvements to tomogram quality, both using best-case static reconstruction and deformation-vector-field-only reconstruction, particularly in reducing motion blur and capturing dynamical features.