MIRT: a simultaneous reconstruction and affine motion compensation technique for four dimensional computed tomography (4DCT)

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.

DELTA-MRI: Direct deformation Estimation from LongiTudinally Acquired k-space data

Longitudinal MRI is an important diagnostic imaging tool for evaluating the effects of treatment and monitoring disease progression. However, MRI, and particularly longitudinal MRI, is known to be time consuming. To accelerate imaging, compressed sensing (CS) theory has been applied to exploit sparsity, both on single image as on image sequence level. State-of-the-art CS methods however, are generally focused on image reconstruction, and consider analysis (e.g., alignment, change detection) as a post-processing step. In this study, we propose DELTA-MRI, a novel framework to estimate longitudinal image changes {\it directly} from a reference image and subsequently acquired, strongly sub-sampled MRI k-space data. In contrast to state-of-the-art longitudinal CS based imaging, our method avoids the conventional multi-step process of image reconstruction of subsequent images, image alignment, and deformation vector field computation. Instead, the set of follow-up images, along with motion and deformation vector fields that describe their relation to the reference image, are estimated in one go. Experiments show that DELTA-MRI performs significantly better than the state-of-the-art in terms of the normalized reconstruction error.