Speaker
Description
Introduction Diffusion models employed as prior knowledge have demonstrated strong performance in MRI reconstruction. A principal advantage of this probabilistic framework is that the variability across generated samples enables uncertainty quantification. Incorporating the likelihood term directly into the diffusion process, however, yields intractable expressions that are typically approximated using various methods. In this work, we examine the explicit inclusion of the likelihood term and propose the use of the exact likelihood, unaltered by the diffusion process. In addition, we include preconditioning into the Unadjusted Langevin Algorithm (ULA) to achieve fast convergence without step size tuning over different MRI reconstruction problems. Methods A UNet trained on the fastMRI brain dataset via score matching is used as a prior. The likelihood is combined with this prior at each noise level, and sampling is performed using the preconditioned ULA (pULA). Inference is conducted on both Cartesian and radial brain data from a healthy volunteer, acquired on an in-house Siemens 3T scanner, with retrospective undersampling at acceleration factors of 4 and 8. We compare pULA against the standard annealed likelihood approach proposed by Jalal et al. and diffusion posterior sampling introduced by Chung et al. Results pULA outperforms both methods in terms of PSNR and SSIM. In addition the proposed method is more robust to the choice of step size and converges faster than the other methods. Discussion and Outlook The proposed method shows fast and robust posterior sampling over various reconstruction problems outperforming current state-of-the-art methods.