使用预条件未调整朗之万算法实现快速且鲁棒的MR图像重建扩散后验采样
Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm
AI总结：
针对MR图像重建中扩散后验采样速度慢和参数调优问题，提出基于预条件未调整朗之万算法的精确似然方法，实现快速收敛且无需调参的鲁棒采样。
摘要：
目的：结合未调整朗之万算法（ULA）与扩散模型，可以从高度欠采样的k空间数据生成高质量MRI重建结果并附带不确定性估计。然而，扩散后验采样（DPS）或似然退火等采样方法存在重建时间长和需要参数调优的问题。本文旨在开发一种具有快速收敛性的鲁棒采样算法。 理论与方法：在用于后验采样的反向扩散过程中，精确似然与所有噪声尺度下的扩散先验相乘。为克服收敛缓慢的问题，采用了预条件技术。该方法在fastMRI数据上训练，并在健康志愿者的回顾性欠采样脑部数据上测试。 结果：对于笛卡尔和非笛卡尔加速MRI的后验采样，新方法在重建速度和样本质量上均优于退火采样和DPS。 结论：所提出的预条件精确似然方法能够在各种MRI重建任务中实现快速可靠的后验采样，无需参数调优。
英文摘要：
Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as diffusion posterior sampling (DPS) or likelihood annealing suffer from long reconstruction times and the need for parameter tuning. The purpose of this work is to develop a robust sampling algorithm with fast convergence. Theory and Methods: In the reverse diffusion process used for sampling the posterior, the exact likelihood is multiplied with the diffused prior at all noise scales. To overcome the issue of slow convergence, preconditioning is used. The method is trained on fastMRI data and tested on retrospectively undersampled brain data of a healthy volunteer. Results: For posterior sampling in Cartesian and non-Cartesian accelerated MRI the new approach outperforms annealed sampling and DPS in terms of reconstruction speed and sample quality. Conclusion: The proposed exact likelihood with preconditioning enables rapid and reliable posterior sampling across various MRI reconstruction tasks without the need for parameter tuning.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
