# A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

arXiv: https://arxiv.org/abs/1812.03446 · HTML: https://mlsanity.com/paper/1812.03446/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2018.

## Built on by (most cited first, 8 of 8)

- [Learning a Model-Driven Variational Network for Deformable Image Registration](https://mlsanity.com/paper/2105.12227/) (2021)
- [Fast MRI Reconstruction via Edge Attention](https://mlsanity.com/paper/2304.11400/) (2023)
- [Retrospective Motion Correction in Gradient Echo MRI by Explicit Motion Estimation Using Deep CNNs](https://mlsanity.com/paper/2303.17239/) (2023)
- [A Bi-variant Variational Model for Diffeomorphic Image Registration with Relaxed Jacobian Determinant Constraints](https://mlsanity.com/paper/2308.02393/) (2023)
- [Joint Manifold Learning and Optimal Transport for Dynamic Imaging](https://mlsanity.com/paper/2505.11913/) (2025)
- [Single-shot Tomography of Discrete Dynamic Objects](https://mlsanity.com/paper/2311.05269/) (2023)
- [SAMCIRT: A Simultaneous Reconstruction and Affine Motion Compensation Technique for Four Dimensional Computed Tomography (4DCT)](https://mlsanity.com/paper/2402.04480/) (2024)
- [A Symmetric Dynamic Learning Framework for Diffeomorphic Medical Image Registration](https://mlsanity.com/paper/2411.02888/) (2024)

## Abstract (arXiv)

We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one for conducting modified static image reconstruction, and the other performs sequentially indirect image registration. For the latter, we generalize the large deformation diffeomorphic metric mapping framework into the sequentially indirect registration setting. The proposed model is compared theoretically against alternative approaches (optical flow based model and diffeomorphic motion models), and we demonstrate that the proposed model has desirable properties in terms of the optimal solution. The theoretical derivations and efficient algorithms are also presented for a time-discretized scenario of the proposed model, which show that the optimal solution of the time-discretized version is consistent with that of the time-continuous one, and most of the computational components is the easy-implemented linearized deformation. The complexity of the algorithm is analyzed as well. This work is concluded by some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data.