# Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction

arXiv: https://arxiv.org/abs/2301.00127 · HTML: https://mlsanity.com/paper/2301.00127/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 75 references that are in the map.
- First posted on arXiv 31 Dec 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [Real-time Neural Radiance Caching for Path Tracing](https://mlsanity.com/paper/2106.12372/) (2021)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [OCMR (v1.0)--Open-Access Multi-Coil k-Space Dataset for Cardiovascular Magnetic Resonance Imaging](https://mlsanity.com/paper/2008.03410/) (2020)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)
- [Deep Learning with Domain Adaptation for Accelerated Projection-Reconstruction MR](https://mlsanity.com/paper/1703.01135/) (2017)
- [Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography](https://mlsanity.com/paper/2209.05483/) (2022)
- [DIMENSION: Dynamic MR Imaging with Both K-space and Spatial Prior Knowledge Obtained via Multi-Supervised Network Training](https://mlsanity.com/paper/1810.00302/) (2018)
- [Dynamic imaging using a deep generative SToRM (Gen-SToRM) model](https://mlsanity.com/paper/2102.00034/) (2021)
- [PARCEL: Physics-based Unsupervised Contrastive Representation Learning for Multi-coil MR Imaging](https://mlsanity.com/paper/2202.01494/) (2022)
- [Variational manifold learning from incomplete data: application to multislice dynamic MRI](https://mlsanity.com/paper/2101.08196/) (2021)
- [SelfCoLearn: Self-supervised collaborative learning for accelerating dynamic MR imaging](https://mlsanity.com/paper/2208.03904/) (2022)

## Built on by (most cited first, 30 of 36)

- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [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)
- [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)
- [MedFuncta: A Unified Framework for Learning Efficient Medical Neural Fields](https://mlsanity.com/paper/2502.14401/) (2025)
- [Moner: Motion Correction in Undersampled Radial MRI with Unsupervised Neural Representation](https://mlsanity.com/paper/2409.16921/) (2024)
- [Subspace Implicit Neural Representations for Real-Time Cardiac Cine MR Imaging](https://mlsanity.com/paper/2412.12742/) (2024)
- [Dynamic-Aware Spatio-temporal Representation Learning for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2501.09049/) (2025)
- [PISCO: Self-Supervised k-Space Regularization for Improved Neural Implicit k-Space Representations of Dynamic MRI](https://mlsanity.com/paper/2501.09403/) (2025)
- [Gabor Primitives for Accelerated Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2603.05681/) (2026)
- [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024)
- [RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging](https://mlsanity.com/paper/2503.10015/) (2025)
- [Disentangled Learning Improves Implicit Neural Representations for Medical Reconstruction](https://mlsanity.com/paper/2605.04234/) (2026)
- [Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow](https://mlsanity.com/paper/2406.01299/) (2024)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [From Coarse to Continuous: Progressive Refinement Implicit Neural Representation for Motion-Robust Anisotropic MRI Reconstruction](https://mlsanity.com/paper/2506.16210/) (2025)
- [Accelerating multiparametric quantitative MRI using self-supervised scan-specific implicit neural representation with model reinforcement](https://mlsanity.com/paper/2508.00891/) (2025)
- [KP-INR: A Dual-Branch Implicit Neural Representation Model for Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2508.12147/) (2025)
- [Self-supervised Deep Unrolled Model with Implicit Neural Representation Regularization for Accelerating MRI Reconstruction](https://mlsanity.com/paper/2510.06611/) (2025)
- [RSTAR4D: Rotational Streak Artifact Reduction in 4D CBCT using a Separable 4D CNN](https://mlsanity.com/paper/2403.16361/) (2024)
- [MR-EIT: Multi-Resolution Reconstruction for Electrical Impedance Tomography via Data-Driven and Unsupervised Dual-Mode Neural Networks](https://mlsanity.com/paper/2503.00762/) (2025)
- [Super-temporal-resolution Photoacoustic Imaging with Dynamic Reconstruction through Implicit Neural Representation in Sparse-view](https://mlsanity.com/paper/2506.03175/) (2025)
- [Low-Rank Augmented Implicit Neural Representation for Unsupervised High-Dimensional Quantitative MRI Reconstruction](https://mlsanity.com/paper/2506.09100/) (2025)
- [Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding](https://mlsanity.com/paper/2507.07707/) (2025)
- [CPT-4DMR: Continuous sPatial-Temporal Representation for 4D-MRI Reconstruction](https://mlsanity.com/paper/2509.18427/) (2025)
- [Flow-Guided Implicit Neural Representation for Motion-Aware Dynamic MRI Reconstruction](https://mlsanity.com/paper/2511.16948/) (2025)
- [Biophysics-Enhanced Neural Representations for Patient-Specific Respiratory Motion Modeling](https://mlsanity.com/paper/2603.22123/) (2026)
- [Model-based Dynamic 3D MRI Reconstructions using Neural Fields and Tensor Product Expansions](https://mlsanity.com/paper/2605.08275/) (2026)
- [MoE-dqINR: A Unified Mixture-of-Experts Implicit Neural Representation Framework for Scan-Specific Dynamic and Quantitative MRI Reconstruction](https://mlsanity.com/paper/2605.31302/) (2026)

## Abstract (arXiv)

Supervised Deep-Learning (DL)-based reconstruction algorithms have shown state-of-the-art results for highly-undersampled dynamic Magnetic Resonance Imaging (MRI) reconstruction. However, the requirement of excessive high-quality ground-truth data hinders their applications due to the generalization problem. Recently, Implicit Neural Representation (INR) has appeared as a powerful DL-based tool for solving the inverse problem by characterizing the attributes of a signal as a continuous function of corresponding coordinates in an unsupervised manner. In this work, we proposed an INR-based method to improve dynamic MRI reconstruction from highly undersampled k-space data, which only takes spatiotemporal coordinates as inputs. Specifically, the proposed INR represents the dynamic MRI images as an implicit function and encodes them into neural networks. The weights of the network are learned from sparsely-acquired (k, t)-space data itself only, without external training datasets or prior images. Benefiting from the strong implicit continuity regularization of INR together with explicit regularization for low-rankness and sparsity, our proposed method outperforms the compared scan-specific methods at various acceleration factors. E.g., experiments on retrospective cardiac cine datasets show an improvement of 5.5 ~ 7.1 dB in PSNR for extremely high accelerations (up to 41.6-fold). The high-quality and inner continuity of the images provided by INR has great potential to further improve the spatiotemporal resolution of dynamic MRI, without the need of any training data.