Hybrid Data-Driven and Physics-Constrained Diffusion for Accelerated Multi-Coil MRI Reconstruction with SVD Coil Compression

Magnetic resonance imaging (MRI) acceleration by k-space undersampling introduces aliasing artifacts. Score-based diffusion models provide strong generative priors but are computationally demanding in multi-coil MRI and may deviate from acquired measurements without explicit constraints. We propose a hybrid data-driven and physics-constrained diffusion framework combining SVD coil compression, reverse-process data consistency, and zero-filled warm-start initialization. SVD projects the measurements into a lower-dimensional virtual-coil subspace, while hard data consistency restores acquired k-space samples after each reverse step. On fastMRI brain data at 4× acceleration, the proposed method achieved 30.70 dB PSNR, 0.7816 SSIM, and 0.0266 NMSE, outperforming the evaluated conventional baselines but remaining below Cascaded-Net in aggregate fidelity. On its 592-slice evaluation subset, a Score-MRI-inspired predictor-corrector reference achieved higher PSNR and lower NMSE, whereas the proposed method achieved higher SSIM. Ablation results showed that data consistency is essential for stable reconstruction. A factor-matched 2 × 2 analysis further showed that the effect of warm-start initialization depends on the data-consistency strategy rather than providing a uniform fidelity improvement.