MIRT: a simultaneous reconstruction and affine motion compensation
  technique for four dimensional computed tomography (4DCT)
Anh-Tuan Nguyen Jens Renders Domenico Iuso Yves Maris Jeroen Soete Martine Wevers Jan Sijbers Jan De Beenhouwer
In four-dimensional computed tomography (4DCT), 3D images of moving or
deforming samples are reconstructed from a set of 2D projection images. Recent
techniques for iterative motion-compensated reconstruction either necessitate a
reference acquisition or alternate image reconstruction and motion estimation
steps. In these methods, the motion estimation step involves the estimation of
either complete deformation vector fields (DVFs) or a limited set of parameters
corresponding to the affine motion, including rigid motion or scaling. The
majority of these approaches rely on nested iterations, incurring significant
computational expenses. Notably, despite the direct benefits of an analytical
formulation and a substantial reduction in computational complexity, there has
been no exploration into parameterizing DVFs for general affine motion in CT
imaging. In this work, we propose the Motion-compensated Iterative
Reconstruction Technique (MIRT)- an efficient iterative reconstruction scheme
that combines image reconstruction and affine motion estimation in a single
update step, based on the analytical gradients of the motion towards both the
reconstruction and the affine motion parameters. When most of the
state-of-the-art 4DCT methods have not attempted to be tested on real data,
results from simulation and real experiments show that our method outperforms
the state-of-the-art CT reconstruction with affine motion correction methods in
computational feasibility and projection distance. In particular, this allows
accurate reconstruction for a proper microscale diamond in the appearance of
motion from the practically acquired projection radiographs, which leads to a
novel application of 4DCT.