[Paper Review] Unsupervised Denoising of Diffusion-Weighted Images with Bias and Variance Corrected Noise Modeling

Jine Xie, Zhicheng Zhang+3 more|arXiv (Cornell University)|Feb 22, 2026

Advanced Neuroimaging Techniques and Applications0 citations

TL;DR

The authors propose two unsupervised loss functions within a Deep Image Prior framework that explicitly model Rician noise in diffusion MRI, correcting bias and heteroscedastic variance to improve denoising and diffusion metrics.

ABSTRACT

Diffusion magnetic resonance imaging (dMRI) plays a vital role in both clinical diagnostics and neuroscience research. However, its inherently low signal-to-noise ratio (SNR), especially under high diffusion weighting, significantly degrades image quality and impairs downstream analysis. Recent self-supervised and unsupervised denoising methods offer a practical solution by enhancing image quality without requiring clean references. However, most of these methods do not explicitly account for the non-Gaussian noise characteristics commonly present in dMRI magnitude data during the supervised learning process, potentially leading to systematic bias and heteroscedastic variance, particularly under low-SNR conditions. To overcome this limitation, we introduce noise-corrected training objectives that explicitly model Rician statistics. Specifically, we propose two alternative loss functions: one derived from the first-order moment to remove mean bias, and another from the second-order moment to correct squared-signal bias. Both losses include adaptive weighting to account for variance heterogeneity and can be used without changing the network architecture. These objectives are instantiated in an image-specific, unsupervised Deep Image Prior (DIP) framework. Comprehensive experiments on simulated and in-vivo dMRI show that the proposed losses effectively reduce Rician bias and suppress noise fluctuations, yielding higher image quality and more reliable diffusion metrics than state-of-the-art denoising baselines. These results underscore the importance of bias- and variance-aware noise modeling for robust dMRI analysis under low-SNR conditions.

Motivation & Objective

• Motivate denoising of diffusion-weighted MRI under low SNR where Rician bias and variance are significant.
• Introduce two bias- and variance-corrected loss functions based on first- and second-moment statistics for magnitude dMRI.
• Leverage an unsupervised Deep Image Prior framework to validate the proposed losses without large training datasets.
• Demonstrate improved image quality and diffusion parameter reliability over state-of-the-art baselines in simulated and in-vivo data.

Proposed method

• Define first-moment and second-moment noise-corrected losses that incorporate adaptive weighting to normalize variance across voxels.
• Formulate DIP-M1-W1 using the first moment and its variance for voxel-wise weighting in the loss.
• Formulate DIP-M2-W2 using the second moment and its variance for voxel-wise weighting in the loss.
• Implement the approach on a 3D U-Net within the DIP framework to denoise 4D dMRI data.
• Compare against MPPCA, Patch2Self, DDM2, and Replace2Self with Rician bias correction for fair evaluation.

Experimental results

Research questions

• RQ1 Can Rician bias and heteroscedastic noise in magnitude dMRI be effectively corrected within an unsupervised DIP framework?
• RQ2 Do first- and second-moment based noise-corrected losses improve denoising quality and diffusion metric reliability over state-of-the-art methods?
• RQ3 How do the proposed losses perform under non-uniform, voxel-wise varying noise conditions?
• RQ4 Do bias- and variance-aware losses preserve fine structural details and yield stable diffusion metrics across resolutions?

Key findings

• DIP-M1-W1 and DIP-M2-W2 reduce Rician bias and suppress noise fluctuations more effectively than baselines in simulated data.
• The proposed losses yield higher PSNR and SSIM for denoised images and lower RMSE with higher SSIM for FA and MD maps.
• Under non-uniform noise, the methods consistently outperform competitors in both image quality and diffusion metric accuracy.
• In-vivo results show robust denoising across resolutions, with better preservation of structural detail and diffusion metric stability (lower COV of FA).
• The approach integrates bias correction within denoising, avoiding error accumulation seen in multi-step baselines.