# Moner: Motion Correction in Undersampled Radial MRI with Unsupervised Neural Representation

arXiv: https://arxiv.org/abs/2409.16921 · HTML: https://mlsanity.com/paper/2409.16921/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 46 references that are in the map.
- First posted on arXiv 25 Sep 2024.

## Builds on (most cited first, 27 of 27)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Local-to-Global Registration for Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2211.11505/) (2022)
- [IREM: High-Resolution Magnetic Resonance (MR) Image Reconstruction via Implicit Neural Representation](https://mlsanity.com/paper/2106.15097/) (2021)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Deep Learning with Domain Adaptation for Accelerated Projection-Reconstruction MR](https://mlsanity.com/paper/1703.01135/) (2017)
- [CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution](https://mlsanity.com/paper/2303.16242/) (2023)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems](https://mlsanity.com/paper/2407.10641/) (2024)
- [Deep Learning for Retrospective Motion Correction in MRI: A Comprehensive Review](https://mlsanity.com/paper/2305.06739/) (2023)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [Cine Cardiac MRI Motion Artifact Reduction Using a Recurrent Neural Network](https://mlsanity.com/paper/2006.12700/) (2020)
- [Accelerated Motion Correction with Deep Generative Diffusion Models](https://mlsanity.com/paper/2211.00199/) (2022)
- [Data Consistent Deep Rigid MRI Motion Correction](https://mlsanity.com/paper/2301.10365/) (2023)
- [ICoNIK: Generating Respiratory-Resolved Abdominal MR Reconstructions Using Neural Implicit Representations in k-Space](https://mlsanity.com/paper/2308.08830/) (2023)
- [Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields](https://mlsanity.com/paper/2307.14363/) (2023)
- [MotionTTT: 2D Test-Time-Training Motion Estimation for 3D Motion Corrected MRI](https://mlsanity.com/paper/2409.09370/) (2024)
- [JSMoCo: Joint Coil Sensitivity and Motion Correction in Parallel MRI with a Self-Calibrating Score-Based Diffusion Model](https://mlsanity.com/paper/2310.09625/) (2023)

## Built on by (most cited first, 4 of 4)

- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [U-Mind: A Unified Framework for Real-Time Multimodal Interaction with Audiovisual Generation](https://mlsanity.com/paper/2602.23739/) (2026)
- [Disentangled Learning Improves Implicit Neural Representations for Medical Reconstruction](https://mlsanity.com/paper/2605.04234/) (2026)
- [Motion Artifact-Aware Self-Supervised Representation Learning for 3D Brain MRI Motion Artifact Reduction](https://mlsanity.com/paper/2608.10170/) (2026)

## Abstract (arXiv)

Motion correction (MoCo) in radial MRI is a particularly challenging problem due to the unpredictability of subject movement. Current state-of-the-art (SOTA) MoCo algorithms often rely on extensive high-quality MR images to pre-train neural networks, which constrains the solution space and leads to outstanding image reconstruction results. However, the need for large-scale datasets significantly increases costs and limits model generalization. In this work, we propose Moner, an unsupervised MoCo method that jointly reconstructs artifact-free MR images and estimates accurate motion from undersampled, rigid motion-corrupted k-space data, without requiring any training data. Our core idea is to leverage the continuous prior of implicit neural representation (INR) to constrain this ill-posed inverse problem, facilitating optimal solutions. Specifically, we integrate a quasi-static motion model into the INR, granting its ability to correct subject's motion. To stabilize model optimization, we reformulate radial MRI reconstruction as a back-projection problem using the Fourier-slice theorem. Additionally, we propose a novel coarse-to-fine hash encoding strategy, significantly enhancing MoCo accuracy. Experiments on multiple MRI datasets show our Moner achieves performance comparable to SOTA MoCo techniques on in-domain data, while demonstrating significant improvements on out-of-domain data. The code is available at: https://github.com/iwuqing/Moner