Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin...

Area of Science:

• Medical Imaging
• Artificial Intelligence
• Computational Science

Background:

• Diffusion models combined with the Unadjusted Langevin Algorithm (ULA) enable high-quality MRI reconstructions and uncertainty estimation from undersampled k-space data.
• Current sampling methods like diffusion posterior sampling (DPS) and likelihood annealing are slow and require extensive parameter tuning.

Purpose of the Study:

• To develop a robust and fast-converging sampling algorithm for MRI reconstruction.
• To address the limitations of existing diffusion model-based sampling techniques.

Main Methods:

• A novel sampling algorithm is proposed, incorporating the exact likelihood with a preconditioned reverse diffusion process.
• The method multiplies the exact likelihood with the diffused prior across all noise scales, utilizing preconditioning to enhance convergence speed.
• The algorithm was trained on fastMRI data and validated on retrospectively undersampled brain MRI data.

Main Results:

• The new approach demonstrates superior reconstruction speed and sample quality compared to annealed sampling and DPS for both Cartesian and non-Cartesian accelerated MRI.
• The proposed method achieves rapid and reliable posterior sampling.

Conclusions:

• The developed exact likelihood with preconditioning offers a significant advancement in MRI reconstruction.
• This method enables fast and reliable posterior sampling for diverse MRI tasks without the need for parameter tuning.