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Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models

Sriram Ravula, Brett Levac, Yamin Arefeen, Ajil Jalal, Alexandros G. Dimakis, Jonathan I. Tamir

TL;DR

This work tackles the challenge of long MRI acquisition times by integrating diffusion-based priors into sampling pattern design. It introduces a one-step posterior mean objective that enables gradient-based learning of Cartesian k-space patterns without backpropagating through costly posterior sampling, and implements a greedy algorithm to construct informative, well-spaced sampling sets. A diffusion-model prior is used in a frozen form, with a Tweedie-extension loss that incorporates measurements to produce a tractable training signal for pattern optimization. Empirically, the approach yields higher reconstruction quality than fixed Poisson-disc or LOUPE-based baselines across multiple anatomies, contrasts, and acceleration factors, demonstrating robust gains and practical applicability in diffusion-based MRI pipelines. The method offers a flexible, non-end-to-end alternative to jointly training reconstruction and sampling, with potential extensions to pattern distributions and higher-dimensional sampling operators.

Abstract

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.

Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models

TL;DR

This work tackles the challenge of long MRI acquisition times by integrating diffusion-based priors into sampling pattern design. It introduces a one-step posterior mean objective that enables gradient-based learning of Cartesian k-space patterns without backpropagating through costly posterior sampling, and implements a greedy algorithm to construct informative, well-spaced sampling sets. A diffusion-model prior is used in a frozen form, with a Tweedie-extension loss that incorporates measurements to produce a tractable training signal for pattern optimization. Empirically, the approach yields higher reconstruction quality than fixed Poisson-disc or LOUPE-based baselines across multiple anatomies, contrasts, and acceleration factors, demonstrating robust gains and practical applicability in diffusion-based MRI pipelines. The method offers a flexible, non-end-to-end alternative to jointly training reconstruction and sampling, with potential extensions to pattern distributions and higher-dimensional sampling operators.

Abstract

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.
Paper Structure (30 sections, 2 theorems, 23 equations, 10 figures, 1 algorithm)

This paper contains 30 sections, 2 theorems, 23 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Compressed Sensing with Generative Models
  4. MRI Sampling Pattern Selection
  5. Background
  6. MRI Reconstruction
  7. Diffusion-Based Generative Models
  8. Accelerated MRI Reconstruction with Diffusion Models
  9. Sampling Pattern Optimization
  10. Methods
  11. Loss Formulation
  12. Learning Sampling Patterns
  13. Experimental Details
  14. Dataset
  15. Diffusion Models
  16. ...and 15 more sections

Key Result

Proposition 1

Let ${\mathbf x}_0 \sim p_0({\mathbf x}_0)$ be an unknown signal, ${\mathbf x}_t \sim p_t({\mathbf x}_t | {\mathbf x}_0) = {\cal N}({\mathbf x}_t; {\mathbf x}_0, \sigma^2_t {\mathbf I})$ a version of ${\mathbf x}_0$ corrupted by additive Gaussian noise, and ${\mathbf y} \sim p({\mathbf y} | {\mathbf

Figures (10)

  • Figure 1: Sampling patterns from different methods for T2 brain data. Optimized sampling patterns from our full proposed method used for reconstructing slices at acceleration factors $R$ in $\{4, 8, 16\}$ with the diffusion-based methods. Poisson Disc sampling tends to distribute samples more uniformly at high acceleration rates, while LOUPE concentrates many samples near the center of k-space. The proposed method balances these effects by maintaining spacing between samples while preferentially allocating measurements to informative central regions.
  • Figure 2: Overview of our method for learning sampling patterns. Starting with the autocalibration region, we greedily grow a set $\mathcal{H}$ (shown in green in the figure) of k-space sampling locations on the Cartesian grid. At each training iteration, we generate a pattern with proper acceleration $R=\frac{m}{n}$ using the previously selected points from $\mathcal{H}$ along with randomly chosen candidate points in k-space that have not yet been added to $\mathcal{H}$. Then, we use the generated pattern in our diffusion training objective to get a loss term and calculate the gradient of the loss at each candidate sampling location. Next, we isolate the $K$ candidate points with the smallest (i.e., largest negative) gradient values, select the point that is farthest away (in terms of Euclidean distance) from its nearest neighbor in $\mathcal{H}$, and finally add that point to $\mathcal{H}$. Our training proceeds, adding one k-space location at a time, until $|\mathcal{H}| = m$ and our desired acceleration is reached.
  • Figure 3: Example Reconstructions from different diffusion methods. We present reconstructions of PDFS knee slice, T2 brain slice, and PD knee slice, all from the test set at $R=20$. Each subfigure includes a zoomed-in region to show fine details (top-left corner) and quantitative metrics (lower-right corner). Reconstructions from our full method, which combines the proposed objective and sampling optimization strategy, achieves better quantitative and qualitative performance in comparison to the baseline diffusion methods.
  • Figure 4: Reconstructions from different diffusion methods for a PD knee slice from the test set at R=4 and R=16. We display the reconstructed slice along with the corresponding residual image (scaled 10$\times$). We present quantitative metrics for each reconstructed slice in the lower-right corner. Our full method produces reconstructions with fewer errors than reconstructions from baseline diffusion methods.
  • Figure 5: Reconstructions from different diffusion methods for a T2 brain slice from the test set at R=4 and R=16. We display the reconstructed slice along with the corresponding residual image (scaled 10$\times$). We present quantitative metrics for each reconstructed slice in the lower-right corner. Our full method produces reconstructions with fewer errors than reconstructions from baseline diffusion methods.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Proposition 1: Tweedie's formula with additional measurements
  • Proposition 1: Tweedie's formula with additional measurements
  • proof