# Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models

arXiv: https://arxiv.org/abs/2306.03284 · HTML: https://mlsanity.com/paper/2306.03284/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Instance-Optimal Compressed Sensing via Posterior Sampling](https://mlsanity.com/paper/2106.11438/) (2021)
- [B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI](https://mlsanity.com/paper/2101.11369/) (2021)
- [Extending LOUPE for K-space Under-sampling Pattern Optimization in Multi-coil MRI](https://mlsanity.com/paper/2007.14450/) (2020)
- [Learning the Sampling Pattern for MRI](https://mlsanity.com/paper/1906.08754/) (2019)
- [Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors](https://mlsanity.com/paper/2002.01697/) (2020)
- [Deep J-Sense: Accelerated MRI Reconstruction via Unrolled Alternating Optimization](https://mlsanity.com/paper/2103.02087/) (2021)
- [Learning Optimal K-space Acquisition and Reconstruction using Physics-Informed Neural Networks](https://mlsanity.com/paper/2204.02480/) (2022)
- [Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications](https://mlsanity.com/paper/2110.14703/) (2021)
- [Linear Predictability in MRI Reconstruction: Leveraging Shift-Invariant Fourier Structure for Faster and Better Imaging](https://mlsanity.com/paper/1903.03141/) (2019)
- [Stochastic Optimization of 3D Non-Cartesian Sampling Trajectory (SNOPY)](https://mlsanity.com/paper/2209.11030/) (2022)

## Built on by (most cited first, 2 of 2)

- [Deep Learning for Accelerated and Robust MRI Reconstruction: a Review](https://mlsanity.com/paper/2404.15692/) (2024)
- [Vision-Language Model-Guided Deep Unrolling Enables Personalized, Fast MRI](https://mlsanity.com/paper/2604.06849/) (2026)

## Abstract (arXiv)

Magnetic resonance imaging (MRI) is a powerful medical imaging modality, but long acquisition times limit throughput, patient comfort, and clinical accessibility. Diffusion-based generative models serve as strong image priors for reducing scan-time with accelerated MRI reconstruction and offer robustness across variations in the acquisition model. However, most existing diffusion-based approaches do not exploit the unique ability in MRI to jointly design both the sampling pattern and the reconstruction method. While prior learning-based approaches have optimized sampling patterns for end-to-end unrolled networks, analogous methods for diffusion-based reconstruction have not been established due to the computational burden of posterior sampling. In this work, we propose a method to optimize k-space sampling patterns for accelerated multi-coil MRI reconstruction using diffusion models as priors. We introduce a training objective based on a single-step posterior mean estimate that avoids backpropagation through an expensive iterative reconstruction process. Then we present a greedy strategy for learning Cartesian sampling patterns that selects informative k-space locations using gradient information from a pre-trained diffusion model while enforcing spatial diversity among samples. Experimental results across multiple anatomies and acceleration factors demonstrate that diffusion models using the optimized sampling patterns achieve higher-quality reconstructions in comparison to using fixed and learned baseline patterns.