Bias-Structure-Correlation Trade off Learning for Self-Supervised Diffusion MRI Denoising

Spatially correlated noise violates the input–target independence assumed by self-supervised diffusion MRI denoising. We identify a three-way trade-off among residual noise correlation, perturbation-induced structural distortion, and model-induced supervision bias, and propose a tensor-guided framework to balance them. By decomposing prediction error into conditional noise bias and structural mismatch, we derive an anisotropy-dependent bound on angular signal distortion under the diffusion tensor model. This bound motivates FA-guided spatio-angular shuffling that limits perturbations in highly anisotropic regions. To address residual noise dependence under restricted perturbations, we introduce a complementary tensor-reconstructed view that excludes the target direction from fitting, preventing direct target-noise reuse. Bidirectional auxiliary guidance and cross-view consistency combine the views to mitigate noise-related and model-induced biases. Experiments on a digital phantom and two in vivo datasets demonstrate improved DW image quality and preservation of diffusion-derived structures. Under 10% Rician noise, our method achieves 34.26 dB PSNR, outperforming the strongest baseline by 0.79 dB, and reduces FA estimation error by approximately 30% relative to the best competing method.