# SAMCIRT: A Simultaneous Reconstruction and Affine Motion Compensation Technique for Four Dimensional Computed Tomography (4DCT)

arXiv: https://arxiv.org/abs/2402.04480 · HTML: https://mlsanity.com/paper/2402.04480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 6 of 6)

- [Core Imaging Library -- Part I: a versatile Python framework for tomographic imaging](https://mlsanity.com/paper/2102.04560/) (2021)
- [Core Imaging Library -- Part II: Multichannel reconstruction for dynamic and spectral tomography](https://mlsanity.com/paper/2102.06126/) (2021)
- [A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging](https://mlsanity.com/paper/1812.03446/) (2018)
- [Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM](https://mlsanity.com/paper/2003.10062/) (2020)
- [Spatiotemporal Besov Priors for Bayesian Inverse Problems](https://mlsanity.com/paper/2306.16378/) (2023)
- [Region-based motion-compensated iterative reconstruction technique for dynamic computed tomography](https://mlsanity.com/paper/2301.11029/) (2023)

## Abstract (arXiv)

The majority of the recent iterative approaches in 4DCT not only rely on nested iterations, thereby increasing computational complexity and constraining potential acceleration, but also fail to provide a theoretical proof of convergence for their proposed iterative schemes. On the other hand, the latest MATLAB and Python image processing toolboxes lack the implementation of analytic adjoints of affine motion operators for 3D object volumes, which does not allow gradient methods using exact derivatives towards affine motion parameters. In this work, we propose the Simultaneous Affine Motion-Compensated Image Reconstruction Technique (SAMCIRT)- an efficient iterative reconstruction scheme that combines image reconstruction and affine motion estimation in a single update step, based on the analytic adjoints of the motion operators then exact partial derivatives with respect to both the reconstruction and the affine motion parameters. Moreover, we prove the separated Lipschitz continuity of the objective function and its associated functions, including the gradient, which supports the convergence of our proposed iterative scheme, despite the non-convexity of the objective function with respect to the affine motion parameters. 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 real, nonstationary diamond, showing a novel application of 4DCT.