Noise-aware adaptive diffusion sampling for accelerated knee MRI reconstruction

We present Noise-Aware adaptive Diffusion sampling (NAD), a novel approach combining classical noise estimation method with diffusion models for accelerated MRI reconstruction. NAD incorporates a noise estimation step based on patch-based Principal Component Analysis (PCA) step that produces a data-consistent least-squares reconstruction as the starting point-thus enabling informed initialization-and guides adaptive sampling in the diffusion process. The method incorporates conjugate gradient-based data consistency updates and controlled noise injection, meaning it re-injects Gaussian noise calibrated to the estimated noise level $\hat{\sigma}(t)$ and scaled by $\gamma$ to efficiently explore the solution space. Evaluated on the Stanford Knee MRI dataset, NAD consistently outperforms state-of-the-art diffusion-based methods in terms of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), while significantly reducing computational time. The proposed method not only advances accelerated MRI reconstruction but also provides insights into efficiently leveraging diffusion models for inverse problems in medical imaging.