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Towards performant and reliable undersampled MR reconstruction via diffusion model sampling
Cheng Peng, Pengfei Guo, S. Kevin Zhou, Vishal Patel, Rama Chellappa
TL;DR
Undersampled MRI can shorten acquisition, but recovering unseen signals is ill-posed and supervised models may be fragile across acceleration factors. DiffuseRecon guides a pretrained diffusion model with observed signals and uses coarse-to-fine sampling to estimate likely reconstructions and their variability. The authors report better performance than current SoTA methods on raw acquisition data.
Problem
Undersampled MR reconstruction must recover unseen k-space in an ill-posed problem, while supervised models can be unreliable across acceleration factors and do not show alternative valid solutions.
Source: §1 · p. 1Method
DiffuseRecon guides a pretrained diffusion model with observed k-space during reverse diffusion and uses coarse-to-fine sampling to estimate likely reconstructions and their variability.
Source: §1 · pp. 2–3Results
DiffuseRecon achieves better performance than current SoTA methods on raw acquisition data, including across different sampling conditions.
Source: §4 · p. 9Takeaways & Limitations
The method produces realistic reconstructions and exposes reconstruction variation, while its sampling scheme estimates a likely candidate and variance.
Source: §3 · p. 8, §4 · p. 9DiffuseRecon requires 1000 inference steps, taking about 20 seconds per slice despite a 20 ms one-time inference speed.
Source: §3 · p. 8
Abstract
from arXiv · showhide
Magnetic Resonance (MR) image reconstruction from under-sampled acquisition promises faster scanning time. To this end, current State-of-The-Art (SoTA) approaches leverage deep neural networks and supervised training to learn a recovery model. While these approaches achieve impressive performances, the learned model can be fragile on unseen degradation, e.g. when given a different acceleration factor. These methods are also generally deterministic and provide a single solution to an ill-posed problem; as such, it can be difficult for practitioners to understand the reliability of the reconstruction. We introduce DiffuseRecon, a novel diffusion model-based MR reconstruction method. DiffuseRecon guides the generation process based on the observed signals and a pre-trained diffusion model, and does not require additional training on specific acceleration factors. DiffuseRecon is stochastic in nature and generates results from a distribution of fully-sampled MR images; as such, it allows us to explicitly visualize different potential reconstruction solutions. Lastly, DiffuseRecon proposes an accelerated, coarse-to-fine Monte-Carlo sampling scheme to approximate the most likely reconstruction candidate. The proposed DiffuseRecon achieves SoTA performances reconstructing from raw acquisition signals in fastMRI and SKM-TEA. Code will be open-sourced at www.github.com/cpeng93/DiffuseRecon.
1 Introduction
Undersampling can shorten MRI acquisition, but recovering unseen k-space is ill-posed and supervised models may be unreliable when acceleration factors change. DiffuseRecon guides a pretrained diffusion model with observed signals and uses coarse-to-fine sampling to estimate likely reconstructions and their variability.
1 Introduction
- Undersampling shortens MRI acquisition, but reconstructing the unseen signal is an ill-posed recovery problem.MRI acquisition time is limited by imaging physics and machine quality.Source: §1 · p. 1
- The reconstruction objective balances agreement with observed k-space against a prior on plausible MR images; supervised CNNs learn that prior from paired data.The formulation uses a data-consistency term and a regularization term.Source: §1 · p. 2
- Supervised models trained for particular acceleration factors can degrade when sampling conditions change and usually provide only one estimate despite multiple valid solutions.Observing alternative reconstructions can help practitioners understand variability and make more robust decisions.Source: §1 · p. 2
- DiffuseRecon gradually guides a pretrained diffusion model with observed k-space during reverse diffusion, generating conditional MR reconstructions with one model across sampling conditions.The figure depicts k-Space Guidance incorporating the observed signal during denoising.Source: §1 · p. 2, Figure 1 · p. 3
- The coarse-to-fine Monte Carlo scheme estimates likely reconstructions and their variability with an approximately 40× speed-up over naive sampling; experiments report superior performance on fastMRI and SKM-TEA.The experiments use raw acquisition signals.Source: §1 · p. 3
2 DiffuseRecon
DiffuseRecon combines a pre-trained diffusion prior with k-space guidance to produce data-consistent stochastic MR reconstructions. Its coarse-to-fine sampler averages multiple coarse draws and refines them to accelerate Monte Carlo sampling.
2 DiffuseRecon
- Diffusion models gradually add Gaussian noise to clean images and use a CNN to reverse the process by denoising intermediate images.The model is trained on MR images to generate images following their learned distribution.Source: §2 · p. 3
- K-Space Guidance mixes the observed signal into denoising so outputs satisfy data consistency while following the pre-trained MR image distribution.The resulting samples vary, enabling inspection of reconstruction reliability and applying to any undersampling mask without finetuning.Source: §2 · pp. 3–4
- Monte Carlo sampling can estimate the conditional reconstruction distribution, but generating multiple diffusion samples is computationally costly.A shortened denoising schedule can reduce the steps, though large k tends to produce less-denoised results.Source: §2 · pp. 4–5
- Multiple coarse samples are averaged and then refined with additional denoising steps to remove averaging-induced blurriness.The refinement steps replace observed k-space signals directly in the reconstructions.Source: §2 · p. 5
- C2F sampling gives an approximately k-time speed-up over naive Monte Carlo sampling.Source: §2 · p. 5
3 Experiments
Experiments on raw knee MR acquisition data compare DiffuseRecon with supervised reconstruction methods, test robustness to changed acceleration factors, and examine sampling choices. DiffuseRecon performs better on the reported comparisons, while visualizations show structural detail and reconstruction variability.
3 Experiments
- Evaluation used single-coil raw complex-valued knee data from fastMRI and SKM-TEA, with 6× and 8× undersampling masks.The evaluation splits contained 199 fastMRI subjects and 21 SKM-TEA subjects.Source: §3 · p. 5
- With {T,k,N,Trefine}={4000,40,10,20}, coarse-to-fine sampling achieved approximately 39× speed-up over naive Monte Carlo sampling.The reported configuration is for C2F Sampling.Source: §3 · p. 6
- PSNR increased significantly with larger sample counts; without gradual-noise k-space guidance, N=1 improved and N=10 worsened versus KSG, while refinement reduced averaging blur.The comparisons use the middle fifteen slices from fastMRI evaluation subjects.Source: §3 · p. 6
- DiffuseRecon outperforms dedicated SoTA models at 6×/8× and performs significantly better on unseen 10×/4× inputs, with a larger gap at higher acceleration.Table 1 compares volume-wise results for dedicated 6× and 8× models and tests robustness using 10× and 4× inputs.Source: Table 1 · p. 7, §3 · p. 7
- DiffuseRecon requires more computation than a single inference pass: it uses 1,000 steps, though the reported 20 seconds per slice still accelerates raw acquisition.The authors note that deterministic methods can be combined with DiffuseRecon when variance analysis is needed selectively.Source: §3 · p. 8
- In visual comparisons, DiffuseRecon recovers structural and vertical knee details lost by D5C5 and OUCR, while its variance map shows uncertainty in detail placement.The lost vertical knee pattern is particularly pronounced in the 8× fastMRI results.Source: §3 · pp. 7–8, Figure 4 · p. 8
4 Conclusion
DiffuseRecon combines reverse-diffusion guidance from observed k-space with coarse-to-fine sampling to produce realistic reconstructions and estimate their variance. The authors report better performance than SoTA methods across sampling conditions and say the variance can inform clinical decisions.
4 Conclusion
- DiffuseRecon is reported as high-performing and robust to different acceleration factors, while allowing users to observe reconstruction variations.The authors evaluated it on raw acquisition data and report better performance than SoTA methods that require dedicated training for different sampling conditions.Source: §4 · p. 9
- Observed k-space signals guide reverse-diffusion, and coarse-to-fine sampling estimates a likely reconstruction candidate and its variance.The method stochastically generates realistic MR reconstructions.Source: §4 · p. 9
- The authors say reconstruction variance can help practitioners make more informed clinical decisions; future work includes faster inference and other MR sampling patterns.Source: §4 · p. 9