# MRI Image Reconstruction via Learning Optimization Using Neural ODEs

arXiv: https://arxiv.org/abs/2006.13825 · HTML: https://mlsanity.com/paper/2006.13825/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 14 of 14)

- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [Over-and-Under Complete Convolutional RNN for MRI Reconstruction](https://mlsanity.com/paper/2106.08886/) (2021)
- [Multi-scale Neural ODEs for 3D Medical Image Registration](https://mlsanity.com/paper/2106.08493/) (2021)
- [Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Future](https://mlsanity.com/paper/2108.04543/) (2021)
- [MetaNODE: Prototype Optimization as a Neural ODE for Few-Shot Learning](https://mlsanity.com/paper/2103.14341/) (2021)
- [An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivities](https://mlsanity.com/paper/2109.09738/) (2021)
- [Invertible Sharpening Network for MRI Reconstruction Enhancement](https://mlsanity.com/paper/2206.02838/) (2022)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [Learned Cone-Beam CT Reconstruction Using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2201.07562/) (2022)
- [Meta-Solver for Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.08561/) (2021)
- [Improving Neural ODEs via Knowledge Distillation](https://mlsanity.com/paper/2203.05103/) (2022)
- [Rethinking Dual-Domain Undersampled MRI reconstruction: domain-specific design from the perspective of the receptive field](https://mlsanity.com/paper/2303.10611/) (2023)
- [Interpretable Modeling and Reduction of Unknown Errors in Mechanistic Operators](https://mlsanity.com/paper/2211.01373/) (2022)
- [TC-KANRecon: High-Quality and Accelerated MRI Reconstruction via Adaptive KAN Mechanisms and Intelligent Feature Scaling](https://mlsanity.com/paper/2408.05705/) (2024)

## Abstract (arXiv)

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and solve the desired ODE with the off-the-shelf (fixed) solver to obtain reconstructed images. We extend this model and incorporate the knowledge of off-the-shelf ODE solvers into the network design (learned solvers). We investigate several models based on three ODE solvers and compare models with fixed solvers and learned solvers. Our models achieve better reconstruction results and are more parameter efficient than other popular methods such as UNet and cascaded CNN. We introduce a new way of tackling the MRI reconstruction problem by modeling the continuous optimization dynamics using neural ODEs.