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

TL;DR

This paper introduces a novel unsupervised denoising method for diffusion MRI that explicitly models Rician noise, effectively reducing bias and variance to improve image quality and analysis reliability in low-SNR conditions.

Contribution

It proposes bias- and variance-aware loss functions within a deep image prior framework to enhance unsupervised denoising of dMRI data, addressing non-Gaussian noise characteristics.

Findings

Effective reduction of Rician bias in dMRI images.

Improved diffusion metric reliability under low-SNR conditions.

Outperforms state-of-the-art denoising methods in experiments.

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.