landmark

Score-based diffusion models for accelerated MRI

Hyungjin Chung, Jong Chul Ye · KAIST · 2021-10 · arXiv:2110.05243

Why it matters

Reconstructs undersampled MRI by alternating score-model sampling with a data-consistency projection against the measured k-space. The pixel space here is not a preference but a structural requirement: the solver needs an invertible mapping between image and measurement domain, which a learned latent would break.

What this paper does

read: full text

Before this

Reconstructing undersampled MRI relied on hand-crafted sparsity priors such as compressed sensing, or on supervised networks trained on paired k-space data that had to be retrained for every new sampling pattern.

The problem

The paper addresses reconstructing accelerated MRI from arbitrary undersampling patterns without retraining, while also handling complex-valued data, multi-coil parallel imaging, and providing uncertainty quantification that regression models cannot give.

The idea

Train a single unconditional score model on magnitude images alone, then at inference alternate reverse-diffusion sampling steps with a data-consistency projection that enforces agreement with the measured k-space.

How it works

Generation happens directly in pixel space, with an NCSN++ score network trained by denoising score matching under a variance-exploding SDE on 25,000 fastMRI knee slices. At inference, predictor-corrector sampling (2000 steps by default) alternates with a projection step that adds lambda times the adjoint operator applied to the measurement residual, where the forward operator maps image pixels to subsampled k-space via Fourier transform and coil sensitivities. The paper does not explicitly argue for pixel space over a latent; it never discusses the alternative, since latent diffusion for images was not yet an established paradigm when this was written in October 2021. The pixel-space choice is structurally implied rather than argued for explicitly, since the projection step needs the forward operator to act directly on what the score model outputs, and that operator is only well-defined as a mapping from image pixels to k-space.

Evidence

Evidence is mostly reconstruction-quality metrics rather than downstream clinical task or reader-study evidence, though one downstream detection result is reported. On single-coil complex data at 2D Gaussian 8x undersampling, the method reaches PSNR 29.45 dB and SSIM 0.676 against a supervised U-Net's 19.99 dB and 0.520. On multi-coil parallel imaging at the same setting it reaches PSNR 31.43 dB against E2E-VarNet's 20.97 dB. A separate pathology-detection experiment reports mAP 0.754, matching the 0.754 achieved from fully sampled reference images. No radiologist reader study is reported.

Limitations

The paper concedes multi-coil reconstruction shows some averaging effect compared with single-coil reconstruction, that naive parallel-imaging inference costs c times longer per coil, and that its two multi-coil algorithms trade off differently by sampling pattern, one favoring 1D masks and the other 2D. Reconstruction already takes about 10 minutes for real-valued and 20 minutes for complex data at 2000 sampling steps.

Why it matters

One trained prior generalizes across any undersampling pattern without retraining, decoupling the learned image model from the measurement operator. Because sampling is generative rather than a point estimate, it also yields uncertainty quantification that standard supervised regression cannot provide.

Abstract, in the authors' own words

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given the measurements, such that the model can be readily used for solving inverse problems in imaging, especially for accelerated MRI. In short, we train a continuous time-dependent score function with denoising score matching. Then, at the inference stage, we iterate between numerical SDE solver and data consistency projection step to achieve reconstruction. Our model requires magnitude images only for training, and yet is able to reconstruct complex-valued data, and even extends to parallel imaging. The proposed method is agnostic to sub-sampling patterns, and can be used with any sampling schemes. Also, due to its generative nature, our approach can quantify uncertainty, which is not possible with standard regression settings. On top of all the advantages, our method also has very strong performance, even beating the models trained with full supervision. With extensive experiments, we verify the superiority of our method in terms of quality and practicality.

Research line

Medical: pixel spacedominant

Method note — the shared flow-matching interpolation

Every flow-matching / rectified-flow paper in this atlas trains toward a straight-line path between a noise sample x₀ and a data sample x₁:

x_t = (1-t)\,x_0 + t\,x_1, \qquad v_\theta(x_t, t) \approx x_1 - x_0

Builds on

Nothing recorded yet.

Built on by

Nothing recorded yet.