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Score-based Self-supervised MRI Denoising

Jiachen Tu, Yaokun Shi, Fan Lam

TL;DR

This work tackles MRI denoising in settings where clean high-SNR labels are unavailable by introducing Corruption2Self (C2S), a score-based self-supervised framework. Central to C2S is Generalized Denoising Score Matching (GDSM), which learns from noisy observations by modeling the conditional expectation $\mathbb{E}[X_{t_{target}} | X_t]$, and unifies DSM, ADSM, and Noisier2Noise as special cases through a forward corruption process and a reparameterized noise schedule. A detail refinement extension balances aggressive noise removal with preservation of fine spatial features, while a multi-contrast extension leverages complementary information across MRI contrasts. The architecture combines a time-conditioned U-Net with Noise Variance Conditioned MSA to adapt to varying noise levels and demonstrates state-of-the-art self-supervised performance and competitive results with supervised methods on M4Raw and fastMRI under diverse noise conditions and contrasts. The approach also exhibits robustness to noise-level estimation errors, suggesting practical applicability as a blind denoising method in clinical MRI workflows.

Abstract

Magnetic resonance imaging (MRI) is a powerful noninvasive diagnostic imaging tool that provides unparalleled soft tissue contrast and anatomical detail. Noise contamination, especially in accelerated and/or low-field acquisitions, can significantly degrade image quality and diagnostic accuracy. Supervised learning based denoising approaches have achieved impressive performance but require high signal-to-noise ratio (SNR) labels, which are often unavailable. Self-supervised learning holds promise to address the label scarcity issue, but existing self-supervised denoising methods tend to oversmooth fine spatial features and often yield inferior performance than supervised methods. We introduce Corruption2Self (C2S), a novel score-based self-supervised framework for MRI denoising. At the core of C2S is a generalized denoising score matching (GDSM) loss, which extends denoising score matching to work directly with noisy observations by modeling the conditional expectation of higher-SNR images given further corrupted observations. This allows the model to effectively learn denoising across multiple noise levels directly from noisy data. Additionally, we incorporate a reparameterization of noise levels to stabilize training and enhance convergence, and introduce a detail refinement extension to balance noise reduction with the preservation of fine spatial features. Moreover, C2S can be extended to multi-contrast denoising by leveraging complementary information across different MRI contrasts. We demonstrate that our method achieves state-of-the-art performance among self-supervised methods and competitive results compared to supervised counterparts across varying noise conditions and MRI contrasts on the M4Raw and fastMRI dataset.

Score-based Self-supervised MRI Denoising

TL;DR

This work tackles MRI denoising in settings where clean high-SNR labels are unavailable by introducing Corruption2Self (C2S), a score-based self-supervised framework. Central to C2S is Generalized Denoising Score Matching (GDSM), which learns from noisy observations by modeling the conditional expectation , and unifies DSM, ADSM, and Noisier2Noise as special cases through a forward corruption process and a reparameterized noise schedule. A detail refinement extension balances aggressive noise removal with preservation of fine spatial features, while a multi-contrast extension leverages complementary information across MRI contrasts. The architecture combines a time-conditioned U-Net with Noise Variance Conditioned MSA to adapt to varying noise levels and demonstrates state-of-the-art self-supervised performance and competitive results with supervised methods on M4Raw and fastMRI under diverse noise conditions and contrasts. The approach also exhibits robustness to noise-level estimation errors, suggesting practical applicability as a blind denoising method in clinical MRI workflows.

Abstract

Magnetic resonance imaging (MRI) is a powerful noninvasive diagnostic imaging tool that provides unparalleled soft tissue contrast and anatomical detail. Noise contamination, especially in accelerated and/or low-field acquisitions, can significantly degrade image quality and diagnostic accuracy. Supervised learning based denoising approaches have achieved impressive performance but require high signal-to-noise ratio (SNR) labels, which are often unavailable. Self-supervised learning holds promise to address the label scarcity issue, but existing self-supervised denoising methods tend to oversmooth fine spatial features and often yield inferior performance than supervised methods. We introduce Corruption2Self (C2S), a novel score-based self-supervised framework for MRI denoising. At the core of C2S is a generalized denoising score matching (GDSM) loss, which extends denoising score matching to work directly with noisy observations by modeling the conditional expectation of higher-SNR images given further corrupted observations. This allows the model to effectively learn denoising across multiple noise levels directly from noisy data. Additionally, we incorporate a reparameterization of noise levels to stabilize training and enhance convergence, and introduce a detail refinement extension to balance noise reduction with the preservation of fine spatial features. Moreover, C2S can be extended to multi-contrast denoising by leveraging complementary information across different MRI contrasts. We demonstrate that our method achieves state-of-the-art performance among self-supervised methods and competitive results compared to supervised counterparts across varying noise conditions and MRI contrasts on the M4Raw and fastMRI dataset.
Paper Structure (44 sections, 5 theorems, 65 equations, 13 figures, 10 tables, 3 algorithms)

This paper contains 44 sections, 5 theorems, 65 equations, 13 figures, 10 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Learning-based denoising without clean targets
  4. Denoising Score Matching
  5. Methodology
  6. Generalized Denoising Score Matching
  7. Corruption2Self: A Score-based Self-supervised MRI Denoising Framework
  8. Results and Discussion
  9. Extending C2S to Multi-Contrast Settings
  10. Conclusion
  11. Additional Experimental Details
  12. Datasets
  13. Training Parameters
  14. Evaluation Protocol
  15. Theoretical Results
  16. ...and 29 more sections

Key Result

Theorem 1

Let $\mathbf{X}_0 \in \mathbb{R}^d$ be a clean data sample drawn from the distribution $p_0(\mathbf{x}_0)$. Suppose that the noisy observation at a given data noise level $t_{\text{data}}$ is and that for any $t > t_{\text{data}}$ the observation $\mathbf{X}_t$ is generated according to the forward process described in Equation equation eq:forward_process. Let $\mathbf{h}_\theta : \mathbb{R}^d \t

Figures (13)

  • Figure 1: Overview of the Corruption2Self (C2S) workflow for MRI denoising. Starting from a noisy MRI image $\mathbf{X}_{t_{\text{data}}}$, the forward corruption process adds additional Gaussian noise to create progressively noisier versions $\mathbf{X}_t$. During training, the model learns to reverse this process by estimating the clean image $\mathbf{X}_0$ from these corrupted observations, despite having access only to noisy data. The denoising function $\mathbf{h}_\theta$ approximates the conditional expectation $\mathbb{E}[\mathbf{X}_0 \mid \mathbf{X}_t]$, effectively learning to denoise without clean targets. A reparameterized function $D_\theta(\mathbf{X}_t, t)$, which shares parameters with $\mathbf{h}_\theta$, is used to compute the loss.
  • Figure 2: Comparison of different denoising methods for T1 contrast from the M4Raw dataset.
  • Figure 3: Comparison of denoising methods for the PD contrast ($\sigma = 13/255$) from the fastMRI dataset.
  • Figure 4: Comparison of different denoising methods for T1 contrast in the M4Raw dataset. The figure showcases Noisy, BM3D, Noise2Noise, and C2S, along with multi-contrast C2S variants (T1 & T2, T1 & FLAIR). Multi-contrast C2S preserves more structural details and produces sharper reconstructions.
  • Figure 5: Comparison of different denoising methods for PD contrast (noise level 13/255) in fastMRI.
  • ...and 8 more figures

Theorems & Definitions (9)

  • Theorem 1: Generalized Denoising Score Matching
  • Remark 1
  • Corollary 2: Reparameterized Generalized Denoising Score Matching
  • Lemma 3
  • proof
  • Theorem 4: Generalized Denoising Score Matching; restated Theorem \ref{['thm_gdsm']}
  • proof
  • Corollary 5: Reparameterized Generalized Denoising Score Matching; restated Corollary \ref{['cor_reparam_gdsm']}
  • proof