Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models

Incoherent k-space undersampling and deep learning-based reconstruction methods have shown great success in accelerating MRI. However, the performance of most previous methods will degrade dramatically under high acceleration factors, e.g., $8\times $ or higher. Recently, denoising diffusion models (DM) have demonstrated promising results in solving this issue; however, one major drawback of the DM methods is the long inference time due to a dramatic number of iterative reverse posterior sampling steps. In this work, a Single Step Diffusion Model-based reconstruction framework, namely SSDM-MRI, is proposed for restoring MRI images from highly undersampled k-space. The proposed method achieves one-step reconstruction by first training a conditional DM and then iteratively distilling this model four times using an iterative selective distillation algorithm, which works synergistically with a shortcut reverse sampling strategy for model inference. Comprehensive experiments were carried out on both publicly available fastMRI brain and knee images, as well as an in-house multi-echo GRE (QSM) subject. Overall, the results showed that SSDM-MRI outperformed other methods in terms of numerical metrics (e.g., PSNR and SSIM), error maps, image fine details, and latent susceptibility information hidden in MRI phase images. In addition, the reconstruction time for a ${320}\times {320}$ brain slice of SSDM-MRI is only 0.45 second, which is only comparable to that of a simple U-net, making it a highly effective solution for MRI reconstruction tasks.