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Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRI

Shoujin Huang, Guanxiong Luo, Xi Wang, Ziran Chen, Yuwan Wang, Huaishui Yang, Pheng-Ann Heng, Lingyan Zhang, Mengye Lyu

TL;DR

The paper tackles diffusion-model–based MRI reconstruction under realistic, inherently noisy acquisition conditions, where a fixed denoising schedule can be misaligned with actual noise levels. It introduces Nila-DC, a noise level adaptive data-consistency operation that linearly attenuates the DC gradient with a parameterized $\lambda_t = kt + b$ to preserve the diffusion prior guidance during reverse diffusion. Reconstruction is cast as Bayesian inversion with a diffusion prior and a likelihood $p(\mathbf{y}|\mathbf{x}) = \mathcal{CN}(\mathbf{y}; \mathcal{A}\mathbf{x}, \sigma_y^2 \mathbf{I})$ under the forward model $\mathbf{y} = \mathcal{A}\mathbf{x} + \boldsymbol{\eta}$, using a learned reverse process $p_\theta(\mathbf{x}_t|\mathbf{x}_{t+1})$. Empirical results on fastMRI, M4Raw, and an in-house 3T dataset show that Nila-DC achieves higher PSNR/SSIM and greater robustness to added noise than L1-wavelet SENSE, CSGM, Spreco, and AdaDiff, including real-world DWI scenarios; the work also discusses practical calibration of $\sigma_y$ and provides code for public use.

Abstract

In general, diffusion model-based MRI reconstruction methods incrementally remove artificially added noise while imposing data consistency to reconstruct the underlying images. However, real-world MRI acquisitions already contain inherent noise due to thermal fluctuations. This phenomenon is particularly notable when using ultra-fast, high-resolution imaging sequences for advanced research, or using low-field systems favored by low- and middle-income countries. These common scenarios can lead to sub-optimal performance or complete failure of existing diffusion model-based reconstruction techniques. Specifically, as the artificially added noise is gradually removed, the inherent MRI noise becomes increasingly pronounced, making the actual noise level inconsistent with the predefined denoising schedule and consequently inaccurate image reconstruction. To tackle this problem, we propose a posterior sampling strategy with a novel NoIse Level Adaptive Data Consistency (Nila-DC) operation. Extensive experiments are conducted on two public datasets and an in-house clinical dataset with field strength ranging from 0.3T to 3T, showing that our method surpasses the state-of-the-art MRI reconstruction methods, and is highly robust against various noise levels. The code for Nila is available at https://github.com/Solor-pikachu/Nila.

Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRI

TL;DR

The paper tackles diffusion-model–based MRI reconstruction under realistic, inherently noisy acquisition conditions, where a fixed denoising schedule can be misaligned with actual noise levels. It introduces Nila-DC, a noise level adaptive data-consistency operation that linearly attenuates the DC gradient with a parameterized to preserve the diffusion prior guidance during reverse diffusion. Reconstruction is cast as Bayesian inversion with a diffusion prior and a likelihood under the forward model , using a learned reverse process . Empirical results on fastMRI, M4Raw, and an in-house 3T dataset show that Nila-DC achieves higher PSNR/SSIM and greater robustness to added noise than L1-wavelet SENSE, CSGM, Spreco, and AdaDiff, including real-world DWI scenarios; the work also discusses practical calibration of and provides code for public use.

Abstract

In general, diffusion model-based MRI reconstruction methods incrementally remove artificially added noise while imposing data consistency to reconstruct the underlying images. However, real-world MRI acquisitions already contain inherent noise due to thermal fluctuations. This phenomenon is particularly notable when using ultra-fast, high-resolution imaging sequences for advanced research, or using low-field systems favored by low- and middle-income countries. These common scenarios can lead to sub-optimal performance or complete failure of existing diffusion model-based reconstruction techniques. Specifically, as the artificially added noise is gradually removed, the inherent MRI noise becomes increasingly pronounced, making the actual noise level inconsistent with the predefined denoising schedule and consequently inaccurate image reconstruction. To tackle this problem, we propose a posterior sampling strategy with a novel NoIse Level Adaptive Data Consistency (Nila-DC) operation. Extensive experiments are conducted on two public datasets and an in-house clinical dataset with field strength ranging from 0.3T to 3T, showing that our method surpasses the state-of-the-art MRI reconstruction methods, and is highly robust against various noise levels. The code for Nila is available at https://github.com/Solor-pikachu/Nila.
Paper Structure (14 sections, 10 equations, 5 figures, 2 tables)

This paper contains 14 sections, 10 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Reconstruction as Bayesian Inversion.
  4. Noise Level Adaptive Data Consistency.
  5. Experiments
  6. Datasets and Baselines.
  7. Training and Evaluation Details.
  8. Quantitative Results.
  9. Qualitative Evaluation.
  10. Real-World DWI Reconstruction.
  11. Ablation Study.
  12. Conclusion
  13. Acknowledgments.
  14. Disclosure of Interests.

Figures (5)

  • Figure 1: General illustration of diffusion model-based MRI reconstruction. Note that the MRI data (measurements) not only contain signals but also noise due to hardware and subject-related thermal fluctuations. This can interfere with the reverse diffusion process, where artificial Gaussian noise is used for image initialization and gradually removed with a pre-defined schedule.
  • Figure 2: Overview of the proposed method. (a) The proposed data consistency (Nila-DC) operation. The computed gradient ($\mathcal{A}^H\mathcal{A}x_t-\mathcal{A}^Hy)$ can be noisy due to MRI noise in $y$ (c.f. Eqs. \ref{['eq7']} and \ref{['eqahay']}) , and is therefore adjusted by a attenuation function (lambda). (b) The attenuation function (c.f. Eq. \ref{['eq:lambda']}) used to rescale the DC gradient. $t$ is the index of the reverse step. (c) The image reconstruction process, where Gaussian noise initialized $x_{t}$ undergoes multi-step reverse diffusion process with the guidance from Nila-DC.
  • Figure 3: Typical reconstructed images. The white numbers indicate the PSNR/SSIM scores. (a) 6$\times$ acceleration on fastMRI. (b) 6$\times$ acceleration on fastMRI with added Gaussian noise. (c) 6$\times$ acceleration on the clinical dataset. Only the proposed method recovered the small white matte lesion as highlighted. (d) 4$\times$ acceleration on M4Raw. CSGM and AdaDiff failed to provide usable images.
  • Figure 4: Reconstruction of prospectively accelerated DWI data. (a) Reconstruction from a single repetition. (b) Averaged from 3 orthogonal diffusion weighting directions, each by 3 repetitions. $\sigma_{y}$ was set to 0.05 for Nila, as estimated from zero-filled reconstruction.
  • Figure 5: Reconstruction of Nila with added noise $\sigma=0.05$ under different settings. (a) Fully sampled image with added $\sigma=0.05$ noise. It is for visualization of the noise level. (b - e) Nila reconstruction using $\sigma_{y}$ values of $0$, $0.025$, $0.05$, and $0.1$, respectively. (d) Fully sampled image without adding extra noise (clean reference). With $\sigma_y$ set to 0, Nila falls back to conventional DDPM-based MRI reconstruction like Eq. \ref{['eq:noise']}. The white numbers indicate the PSNR/SSIM scores of the displayed images.