# A Unified Model for Compressed Sensing MRI Across Undersampling Patterns

arXiv: https://arxiv.org/abs/2410.16290 · HTML: https://mlsanity.com/paper/2410.16290/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions](https://mlsanity.com/paper/2209.13603/) (2022)

## Built on by (most cited first, 7 of 7)

- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Physics-Aware Neural Operators for Direct Inversion in 3D Photoacoustic Tomography](https://mlsanity.com/paper/2509.09894/) (2025)
- [Nirvana: A Specialized Generalist Model With Task-Aware Memory Mechanism](https://mlsanity.com/paper/2510.26083/) (2025)
- [Resolution-Agnostic Neural Operators for Multi-Rate Sparse-View CT](https://mlsanity.com/paper/2512.12236/) (2025)
- [Self-Supervised Learning via Flow-Guided Neural Operator on Time-Series Data](https://mlsanity.com/paper/2602.12267/) (2026)
- [UEPS: Robust and Efficient MRI Reconstruction](https://mlsanity.com/paper/2603.18572/) (2026)
- [SONAR: A Structure-Consistent Neural Operator for Null-Space-Aware Sparse View CT Reconstruction](https://mlsanity.com/paper/2609.13688/) (2026)

## Abstract (arXiv)

Compressed Sensing MRI reconstructs images of the body's internal anatomy from undersampled measurements, thereby reducing scan time. Recently, deep learning has shown great potential for reconstructing high-fidelity images from highly undersampled measurements. However, one needs to train multiple models for different undersampling patterns and desired output image resolutions, since most networks operate on a fixed discretization. Such approaches are highly impractical in clinical settings, where undersampling patterns and image resolutions are frequently changed to accommodate different real-time imaging and diagnostic requirements. We propose a unified MRI reconstruction model robust to various measurement undersampling patterns and image resolutions. Our approach uses neural operators, a discretization-agnostic architecture applied in both image and measurement spaces, to capture local and global features. Empirically, our model improves SSIM by 11% and PSNR by 4 dB over a state-of-the-art CNN (End-to-End VarNet), with 600× faster inference than diffusion methods. The resolution-agnostic design also enables zero-shot super-resolution and extended field-of-view reconstruction, offering a versatile and efficient solution for clinical MR imaging. Our unified model offers a versatile solution for MRI, adapting seamlessly to various measurement undersampling and imaging resolutions, making it highly effective for flexible and reliable clinical imaging. Our code is available at https://armeet.ca/nomri.