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.Comment: Submitted to the SIAM Journal on Imaging Sciences (SIIMS

Rosenberg's Reconstruction Theorem (after Gabber)

Alexander L. Rosenberg has constructed a spectrum for abelian categories which is able to reconstruct a quasi-separated scheme from its abelian category of quasi-coherent sheaves. In this note we present a detailed proof of this result which is due to Ofer Gabber.Comment: 18 pages; revised Thm 5.

Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.Comment: 21 pages, 16 figure