Towards Data-Informed Motion Artifact Reduction in Quantitative CT Using Piecewise Linear Interpolation

We propose to use piecewise linear interpolation (PLI) in time to reduce motion artifacts in transmission computed tomography (CT). PLI is motivated by the natural occurrence of piecewise-linear evolution of voxel values during object motion. The method is specifically examined in the context of high-accuracy quantitative measurements that are compromised by small motions, and particularly sub-pixel motion. Compared to existing methods, the proposed approach offers three advantages: (i) the flexibility in the interpolation parameters provides a framework for joint optimization and data-informed dynamic CT, (ii) both continuous motion and sudden changes in voxel values can be represented while preserving the continuity of the interpolated solution, and (iii) the compactness of the interpolation functions reduces the increase in algorithmic cost. Total variation regularization is used with a second-order accurate discretization, and the resulting formulation is solved with the Chamholle-Pock proximal algorithm. The applicability of the method in practical cases is demonstrated using synchrotron data, with an algorithmic cost of two to four times that of equivalent static reconstruction algorithms.