Adaptive physics-inspired angular-spatial modeling for multi-shell diffusion MRI denoising

Abstract

Abstract Objective. Multi-shell diffusion magnetic resonance imaging (dMRI) provides rich q-space information but is susceptible to noise, which can disrupt spatial anatomy, intra-shell directional relationships, inter-shell signal attenuation, and downstream diffusion parameter estimation. We aim to develop a denoising method that jointly preserves spatial structure, directional information, and shell-specific signal characteristics. Approach. We propose ASD-NCSM, an adaptive physics-inspired angular-spatial framework with a fixed three-stage alternating architecture. It combines intra-shell differential angular graph message passing with 2.5D spatial residual refinement. Noise-Conditioned Shell Modulation (NCSM) adaptively regulates angular updates according to b-value, spatial residual and angular dispersion proxies, and local gating. A Shell-wise Physical Attenuation and Angular Relation Consistency (SPARC) objective further constrains shell-wise signal fidelity, logarithmic attenuation, and local angular structure. The model was evaluated on HCP multi-shell dMRI with simulated noise and independently acquired real in vivo brain dMRI data. Main results. Across five simulated noise levels from 2% to 10%, ASD-NCSM achieved the best overall DWI restoration among MPPCA, 1D-CNN, ECDM, SAN2N, and dMRI-Swin, with consistent subject-level advantages in PSNR, SSIM, and NRMSE. At 6% noise, principal-direction angular nRMSE was 32.68 ± 2.76%, with significant differences from all five baselines after Holm correction. ASD-NCSM also achieved the lowest mean MAE for FA, MD, AD, and RD, and the lowest relative MAE for ODI and FISO, while NDI was comparable to 1D-CNN and dMRI-Swin. For real data without noise-free references, Q-PEFT yielded the lowest angular cross-fit inconsistency (2.29 ± 0.10%) across three test subjects while maintaining limited signal and downstream-parameter changes. Significance. ASD-NCSM jointly preserves spatial continuity, directional geometry, and shell-level attenuation, providing balanced signal recovery, directional preservation, and downstream parameter stability for multi-shell dMRI denoising.