Organizations: School of Biomedical Engineering, Southern Medical University, Guangzhou, China · Guangdong Provincial Key Laboratory of Medical Image Processing, Southern Medical University, Guangzhou, China · JancsiLab, JancsiTech, Hong Kong, China · Department of Radiation Oncology, Sun Yat-sen University Cancer Center, Guangzhou, China
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 & tables
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.
Figure 6: Visual comparison of DW images ( b=1500 and 3000s/mm2 ) and FA maps from different methods, using the first in-vivo data with three different resolutions.
Figure 7: Comparison of the coefficient of variation (COV) for FA values across different brain regions from different methods, using the first in-vivo data with three different resolutions.
Figure 8: A visual comparison of DW image, FA, color-FA, and their corresponding enlarged maps for different methods, using the second in-vivo data.
Figure 9: Comparison of DW images and SANDI parameter maps ( fin , fis , and Rs ) generated by different denoising methods from the third in-vivo data with ultra-high b-values.
Figure 10: Quantitative comparisons of different DIP-based methods on the simulated dataset with different noise levels, for the denoised dMRI data and the derived DTI parameters (FA and MD).
Figure 11: Quantitative comparisons of DIP-M1-W1 and DIP-M2-W2 on the denoised dMRI data and derived DTI parameters (FA and MD), using different noise estimation ( σ^ ) on the simulated data with a true noise level of 0.05 ( σ^=0 : the original DIP).
Figure 12: Quantitative comparisons of DIP-M1-W1 and DIP-M2-W2 on the denoised dMRI data and derived DTI parameters (FA and MD), using both MPPCA-estimated and true noise maps on a simulated dataset with spatially varying noise. The lower right corner displays the MPPCA-estimated and true noise maps for the spatially varying noise (0.03-0.05).
Figure 13: Robustness evaluation under random initializations. (a, c) PSNR and SSIM of the denoised images across ten random initializations for DIP-M1-W1 and DIP-M2-W2, respectively. (b, d) Corresponding standard deviation maps derived from the ten denoised b0 images and DW images for DIP-M1-W1 and DIP-M2-W2.
Diffusion-weighted imaging (DWI) is used for whole-body cancer screening, but it typically requires a long acquisition time. When the scan time is reduced, the image quality often suffers, leading to increased noise in the scans. Magnitude reconstruction in DWI introduces signal-dependent Rician noise, which makes denoising more challenging for conventional convolution-based methods. To address this limitation, we propose a noise-aware attention-driven denoising framework that integrates hierarchical Swin Transformer window attention with transformer-based multi-dimensional gated refinement for DWI restoration. The model incorporates explicit noise-level conditioning and residual reconstruction to enable adaptive suppression of heteroscedastic noise across a wide range of corruption levels. Experimental evaluation on corrupted DWI scans demonstrates strong restoration performance. Our model achieves a mean PSNR of 33.69~dB and SSIM of 0.8539 across noise levels from 1% to 15%, while maintaining stable behavior under severe noise conditions. These results indicate that attention-guided contextual modeling combined with channel-adaptive refinement provides a robust and generalizable solution for DWI denoising.
Prithviraj Verma, Pawan Kumar, Chandan Deshani +1
Institute of Infrastructure Technology Research and Management (IITRAM), India · University of Sheffield, United Kingdom
Diffusion MRI enables non-invasive probing of tissue microstructure, but accurate parameter estimation is challenged by noise-related effects. In supervised machine learning frameworks trained on simulated data, discrepancies between the noise characteristics of simulated and acquired signals introduce a form of covariate shift, whereby the input signal distribution differs between training and inference. We investigated the impact of this mismatch on microstructure parameter estimation and propose a realistic noise synthesis (RNS) framework to mitigate it. RNS incorporates both the Rician expectation and the effective post-processing noise variance into simulated training signals. The Rician expectation was modelled using a noise standard deviation estimated with MPPCA, while the effective standard deviation was derived from spherical harmonic residuals of preprocessed data. The method was evaluated using the cylinder-zeppelin and the SANDI models on simulated datasets across multiple SNR levels and on in vivo diffusion data with repeated acquisitions. Sensitivity to noise misestimation was also assessed. Ignoring magnitude-induced noise effects during training produced systematic, SNR-dependent parameter bias, particularly at low SNR. Incorporating the Rician expectation substantially reduced bias to the level of noise-aware nonlinear least-squares fitting. Modelling the effective standard deviation further improved precision. Performance was largely independent of regression architecture but sensitive to accurate noise estimation. These findings demonstrate that realistic noise modelling in simulated training data mitigates signal-domain covariate shift and is essential for unbiased supervised microstructure estimation, particularly in low-SNR regimes associated with high b-values or high spatial resolution.
Bradley G. Karat, Maëliss Jallais, Ali R. Khan +3
Robarts Research Institute, Schulich School of Medicine and Dentistry, The University of Western Ontario, London, Canada · Center for Biomedical Imaging, Department of Radiology, NYU Grossman School of Medicine, New York, New York, USA · Cardiff University Brain Research Imaging Center (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom +3
Magnetic resonance imaging involves an inherent trade-off among spatial resolution, acquisition time, and noise. This trade-off contributes to long scan times and high cost. Deep learning has improved image denoising, but cardiac MRI remains difficult because high-resolution, rapid acquisitions generally lack corresponding low-noise ground truth. Self-supervised denoising offers a potential solution by learning from noisy image pairs or even single noisy acquisitions. However, we show that Noise2Void-style blind-spot denoising, which uses a mean squared error (MSE) loss and assumes zero-mean, independent and identically distributed (i.i.d.) noise, is poorly suited to MR magnitude images. When applied to short-axis T2-weighted and T1ρ-weighted cardiac MRI with synthetic Rician noise, it produces biased denoised images and biased parametric maps of T2 and T1ρ. To address this limitation, we formulate self-supervised denoising as maximum likelihood estimation under a known Rician noise model. This yields unbiased denoisers that are competitive with supervised baselines.