# NeRF Solves Undersampled MRI Reconstruction

arXiv: https://arxiv.org/abs/2402.13226 · HTML: https://mlsanity.com/paper/2402.13226/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [PS-NeRF: Neural Inverse Rendering for Multi-view Photometric Stereo](https://mlsanity.com/paper/2207.11406/) (2022)
- [Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge](https://mlsanity.com/paper/2001.02518/) (2020)
- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Deep Learning-Based Solvability of Underdetermined Inverse Problems in Medical Imaging](https://mlsanity.com/paper/2001.01432/) (2020)
- [Framelet Pooling Aided Deep Learning Network : The Method to Process High Dimensional Medical Data](https://mlsanity.com/paper/1907.10834/) (2019)

## Built on by (most cited first, 1 of 1)

- [INFusion: Diffusion Regularized Implicit Neural Representations for 2D and 3D accelerated MRI reconstruction](https://mlsanity.com/paper/2406.13895/) (2024)

## Abstract (arXiv)

This article presents a novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF). With radial undersampling, the corresponding imaging problem can be reformulated into an image modeling task from sparse-view rendered data; therefore, a high dimensional MR image is obtainable from undersampled k-space data by taking advantage of implicit neural representation. A multi-layer perceptron, which is designed to output an image intensity from a spatial coordinate, learns the MR physics-driven rendering relation between given measurement data and desired image. Effective undersampling strategies for high-quality neural representation are investigated. The proposed method serves two benefits: (i) The learning is based fully on single undersampled k-space data, not a bunch of measured data and target image sets. It can be used potentially for diagnostic MR imaging, such as fetal MRI, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded. (ii) A reconstructed MR image is a scan-specific representation highly adaptive to the given k-space measurement. Numerous experiments validate the feasibility and capability of the proposed approach.