# Model-based Dynamic 3D MRI Reconstructions using Neural Fields and Tensor Product Expansions

arXiv: https://arxiv.org/abs/2605.08275 · HTML: https://mlsanity.com/paper/2605.08275/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 8 May 2026.

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

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [OCMR (v1.0)--Open-Access Multi-Coil k-Space Dataset for Cardiovascular Magnetic Resonance Imaging](https://mlsanity.com/paper/2008.03410/) (2020)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [The state-of-the-art in Cardiac MRI Reconstruction: Results of the CMRxRecon Challenge in MICCAI 2023](https://mlsanity.com/paper/2404.01082/) (2024)
- [Motion-robust free-running volumetric cardiovascular MRI](https://mlsanity.com/paper/2308.02088/) (2023)

## Abstract (arXiv)

Conventional MRI reconstruction methods treat images and coil sensitivities as discrete objects, leading to high memory demands and limited structural awareness that hamper effective regularization. These limitations hinder accurate reconstruction in highly undersampled scenarios, such as dynamic 3D cardiac magnetic resonance (CMR). We introduce a discretization-free, memory-efficient, model-based framework for dynamic 2D and 3D MRI reconstruction from highly undersampled data. We represent magnetization and coil sensitivities as continuous objects -- differentiable functions -- using tensor products of univariate neural fields. This tensor product structure enables scalable optimization in high-dimensional spatiotemporal settings. Our method outperforms state-of-the-art model-based reconstructions in dynamic 2D and 3D MR settings, preserving structure and motion even under aggressive undersampling (e.g., acceleration factor 16).