Unsupervised Denoising of Diffusion-Weighted Images with Bias and Variance Corrected Noise Modeling

TL;DR

Two alternative loss functions are proposed that effectively reduce Rician bias and suppress noise fluctuations, yielding higher image quality and more reliable diffusion metrics than state-of-the-art denoising baselines and underscore the importance of bias- and variance-aware noise modeling for robust dMRI analysis under low-SNR conditions.

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.

Figures (13)

• Figure 1: Overview of DIP-M1-W1 and DIP-M2-W2 architectures based on 3D U-Net.
• Figure 2: Quantitative comparisons of different methods on the simulated dataset across various noise levels, for the denoised dMRI data and the derived DTI parameters (FA and MD). Dashed lines represent denoised results after applying explicit first-moment Rician bias correction.
• Figure 3: Visual comparison of non-DW (b0) and DW (b1000) images, as well as FA and MD maps, obtained by our methods and by competing methods (both with and without Rician bias correction) ,on the simulated data with a noise level of 0.05. The values highlighted in red indicate the best performance.
• Figure 4: Quantitative evaluation of different methods on simulated dMRI data with spatially varying noise: PSNR and SSIM of dMRI images, and RMSE and SSIM of FA and MD maps.
• Figure 5: Visual comparison of non-DW (b0) and DW (b1000) images, as well as FA and MD maps, obtained by different methods using the simulated data with spatially varying noise (noise level 0.03-0.05). The values highlighted in red indicate the best performance.