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High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction

arXiv 2607.01176 ↗First posted 1 Jul 2026cs.CVcited by 0

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Abstract (arXiv)

Magnetic resonance imaging (MRI) reconstruction under realistic acquisition conditions can be fundamentally viewed as estimating the underlying k-space distribution from incomplete and noise-corrupted measurements. While diffusion models have recently shown strong potential as generative prior for inverse problems,existingapproachesstruggletohandlenoisyreconstruction settings, especially when operating directly in k-space domain. In this work, we propose a unified high-dimensional k-space reconstruction framework tailored for noisy inverse problems, whichenhancesdiffusion-based solversthroughrepresentation lifting.Ratherthanmodifyingthe underlying optimization procedures, the proposed framework augments the data representation space, enabling existing diffusion-based solvers to operate on enriched k-space embeddings with improved expressiveness. Extensive experiments on both in-house and public datasets across varying noise levels and undersampled factors demonstrate that the proposed frame work consistently improves reconstruction quality for multiple diffusion-based inverse solvers. Notably, the largest gains are observed in high-noise regimes, which is consistent with our theoretical analysis of error propagation under high-dimensional representation. These results suggest that high-dimensional representation provides a general and model-agnostic mechanism for improving diffusion-based MRI reconstruction in noisy settings, offering a new perspective on robust k-space generative modeling for practical inverse problems. The code will be available at https://github.com/yqx7150/HEP-MRIRec.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 30 of its 57 references that are in the map. First posted on arXiv 1 Jul 2026.

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References · 30

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  5. 2021Variational Diffusion Modelscited by 1,145
  6. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  7. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  8. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 384
  9. 2017A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstructioncited by 231
  10. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 217
  11. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  12. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
18 more
  1. 2022Adaptive Diffusion Priors for Accelerated MRI Reconstructioncited by 117
  2. 2017Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstructioncited by 105
  3. 2017Deep learning for undersampled MRI reconstructioncited by 91
  4. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusioncited by 78
  5. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 58
  6. 2025Diffusion models for inverse problemscited by 15
  7. 2023Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstructioncited by 14
  8. 2022One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstructioncited by 11
  9. 2023CDiffMR: Can We Replace the Gaussian Noise with K-Space Undersampling for Fast MRI?cited by 11
  10. 2020Joint Frequency and Image Space Learning for MRI Reconstruction and Analysiscited by 10
  11. 2022WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstructioncited by 8
  12. 2024Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRIcited by 6
  13. 2020Sampling possible reconstructions of undersampled acquisitions in MR imagingcited by 5
  14. 2023Learning to Reconstruct Accelerated MRI Through K-space Cold Diffusion without Noisecited by 4
  15. 2024Deep Data Consistency: a Fast and Robust Diffusion Model-based Solver for Inverse Problemscited by 4
  16. 2023High-Dimensional MR Reconstruction Integrating Subspace and Adaptive Generative Modelscited by 3
  17. 2024Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstructioncited by 2
  18. 2026Understanding Generalization from Embedding Dimension and Distributional Convergencecited by 1

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  1. 2023Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models
  2. 2023Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstruction
  3. 2022Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models
  4. 2022High-Frequency Space Diffusion Models for Accelerated MRI
  5. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models
  6. 2024Autoregressive Image Diffusion: Generation of Image Sequence and Application in MRI
  7. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction
  8. 2025Conditional Denoising Diffusion Model-Based Robust MR Image Reconstruction from Highly Undersampled Data