Analytic derivatives of scaling motion-compensated projection operators for dynamic computed tomography

Abstract

This work presents an iterative method in dynamic computed tomography (dynamic CT) which enables accurate reconstruction and scaling correction simultaneously. Recent achievements in dynamic CT have shown the feasibility of reconstructing an image of an object while simultaneously estimating its temporal deformation model parameters. Those approaches consider a mathematical minimization problem whose objective function depends on the reconstruction as well as on the deformation parameters corresponding to the motion model, mostly represented by affine transformations. Nonetheless, they lack a validation on non-rigid motion models wherein the motion is estimated by an objective function whose partial derivatives toward motion parameters are analytical. In this work, those operators are given exactly. Results from simulation and real data experiments show that the blurring artifacts caused by the motion are largely reduced.