# Learned Cone-Beam CT Reconstruction Using Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2201.07562 · HTML: https://mlsanity.com/paper/2201.07562/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [PYRO-NN: Python Reconstruction Operators in Neural Networks](https://mlsanity.com/paper/1904.13342/) (2019)
- [A Cone-Beam X-Ray CT Data Collection designed for Machine Learning](https://mlsanity.com/paper/1905.04787/) (2019)
- [Multi-Scale Learned Iterative Reconstruction](https://mlsanity.com/paper/1908.00936/) (2019)
- [Memory-efficient Learning for Large-scale Computational Imaging -- NeurIPS deep inverse workshop](https://mlsanity.com/paper/1912.05098/) (2019)
- [MRI Image Reconstruction via Learning Optimization Using Neural ODEs](https://mlsanity.com/paper/2006.13825/) (2020)
- [Deep Variational Networks with Exponential Weighting for Learning Computed Tomography](https://mlsanity.com/paper/1906.05528/) (2019)
- [Computationally Efficient Deep Neural Network for Computed Tomography Image Reconstruction](https://mlsanity.com/paper/1810.03999/) (2018)
- [Robust partial Fourier reconstruction for diffusion-weighted imaging using a recurrent convolutional neural network](https://mlsanity.com/paper/2105.09378/) (2021)

## Built on by (most cited first, 3 of 3)

- [3D helical CT Reconstruction with a Memory Efficient Learned Primal-Dual Architecture](https://mlsanity.com/paper/2205.11952/) (2022)
- [Geometric Constraints Enable Self-Supervised Sinogram Inpainting in Sparse-View Tomography](https://mlsanity.com/paper/2302.06436/) (2023)
- [Deep Few-view High-resolution Photon-counting CT at Halved Dose for Extremity Imaging](https://mlsanity.com/paper/2403.12331/) (2024)

## Abstract (arXiv)

Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring consistency with the measured data. In computed tomography, extending such approaches from 2D fan-beam to 3D cone-beam data is challenging due to the prohibitively high GPU memory that would be needed to train such models. This paper proposes to use neural ordinary differential equations to solve the reconstruction problem in a residual formulation via numerical integration. For training, there is no need to backpropagate through several unrolled network blocks nor through the internals of the solver. Instead, the gradients are obtained very memory-efficiently in the neural ODE setting allowing for training on a single consumer graphics card. The method is able to reduce the root mean squared error by over 30% compared to the best performing classical iterative reconstruction algorithm and produces high quality cone-beam reconstructions even in a sparse view scenario.