# Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration

arXiv: https://arxiv.org/abs/2109.12688 · HTML: https://mlsanity.com/paper/2109.12688/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 26 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [DeepFLASH: An Efficient Network for Learning-based Medical Image Registration](https://mlsanity.com/paper/2004.02097/) (2020)

## Built on by (most cited first, 16 of 16)

- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [U-Net vs Transformer: Is U-Net Outdated in Medical Image Registration?](https://mlsanity.com/paper/2208.04939/) (2022)
- [Fourier-Net: Fast Image Registration with Band-limited Deformation](https://mlsanity.com/paper/2211.16342/) (2022)
- [Decoder-Only Image Registration](https://mlsanity.com/paper/2402.03585/) (2024)
- [PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems](https://mlsanity.com/paper/2509.22736/) (2025)
- [Fourier-Net+: Leveraging Band-Limited Representation for Efficient 3D Medical Image Registration](https://mlsanity.com/paper/2307.02997/) (2023)
- [WiNet: Wavelet-based Incremental Learning for Efficient Medical Image Registration](https://mlsanity.com/paper/2407.13426/) (2024)
- [FedMed-ATL: Misaligned Unpaired Brain Image Synthesis via Affine Transform Loss](https://mlsanity.com/paper/2201.12589/) (2022)
- [SACB-Net: Spatial-awareness Convolutions for Medical Image Registration](https://mlsanity.com/paper/2503.19592/) (2025)
- [UMPIRE-Net: Unrolled Magnitude-Phase Regularization Network for Accelerated MRI](https://mlsanity.com/paper/2608.14422/) (2026)
- [Structure Unbiased Adversarial Model for Medical Image Segmentation](https://mlsanity.com/paper/2205.12857/) (2022)
- [Optimizing ADMM and Over-Relaxed ADMM Parameters for Linear Quadratic Problems](https://mlsanity.com/paper/2401.00657/) (2024)
- [An Efficient Model-Driven Groupwise Approach for Atlas Construction](https://mlsanity.com/paper/2508.10743/) (2025)
- [Robust Rigid and Non-Rigid Medical Image Registration Using Learnable Edge Kernels](https://mlsanity.com/paper/2512.01771/) (2025)
- [Plasticine: A Traceable Diffusion Model for Medical Image Translation](https://mlsanity.com/paper/2512.18455/) (2025)
- [Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors](https://mlsanity.com/paper/2608.18036/) (2026)

## Abstract (arXiv)

Deterministic approaches using iterative optimisation have been historically successful in diffeomorphic image registration (DiffIR). Although these approaches are highly accurate, they typically carry a significant computational burden. Recent developments in stochastic approaches based on deep learning have achieved sub-second runtimes for DiffIR with competitive registration accuracy, offering a fast alternative to conventional iterative methods. In this paper, we attempt to reduce this difference in speed whilst retaining the performance advantage of iterative approaches in DiffIR. We first propose a simple iterative scheme that functionally composes intermediate non-stationary velocity fields to handle large deformations in images whilst guaranteeing diffeomorphisms in the resultant deformation. We then propose a convex optimisation model that uses a regularisation term of arbitrary order to impose smoothness on these velocity fields and solve this model with a fast algorithm that combines Nesterov gradient descent and the alternating direction method of multipliers (ADMM). Finally, we leverage the computational power of GPU to implement this accelerated ADMM solver on a 3D cardiac MRI dataset, further reducing runtime to less than 2 seconds. In addition to producing strictly diffeomorphic deformations, our methods outperform both state-of-the-art deep learning-based and iterative DiffIR approaches in terms of dice and Hausdorff scores, with speed approaching the inference time of deep learning-based methods.