用预条件方法加速扩散模型在MRI重建中的采样，无需调参且速度快质量高。
Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm
- 采用预条件无调整Langevin算法，提升后验采样收敛速度。
- 在脑部MRI数据上，重建速度比传统方法快，样本质量更高。
- 适用于各种加速成像任务，无需人工调参，鲁棒性强。
目的：无调整Langevin算法（ULA）结合扩散模型可从高度欠采样的k空间数据中生成高质量的MRI重建结果，并提供不确定性估计。然而，如扩散后验采样（DPS）或似然退火等采样方法存在重建时间长、需参数调优的问题。本文旨在开发一种收敛快速且鲁棒的采样算法。理论与方法：在反向扩散过程中，精确似然在所有噪声尺度下与扩散先验相乘。为解决收敛慢问题，引入预条件机制。方法在fastMRI数据上训练，并在健康志愿者的回溯性欠采样脑部数据上测试。结果：在笛卡尔和非笛卡尔加速MRI中，新方法在重建速度和样本质量上均优于似然退火和DPS。结论：所提出的精确似然结合预条件机制，可在无需参数调优的情况下实现跨多种MRI重建任务的快速可靠后验采样。
原文摘要 · Abstract (English)
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.
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