用混合高斯扩散模型实现快速、可解释的MRI重建，同时估计线圈敏感度。
Product of Gaussian Mixture Diffusion Model for non-linear MRI Inversion
- 采用轻量级混合高斯扩散模型作为图像先验，结合光滑性正则化建模线圈敏感度。
- 在多种采样轨迹和对比度下保持鲁棒，推理速度显著快于传统方法。
- 支持后验均值与像素方差计算，适合需要不确定性估计的应用场景。
扩散模型在磁共振成像重建中表现优异，但其网络通常为参数量达数百万的黑箱先验得分估计器，限制了可解释性并增加重建时间。现有并行成像算法或依赖离线线圈敏感度估计（易发生错位且限制采样轨迹），或进行逐线圈重建（计算开销与线圈数成正比）。为此，本文提出联合重建图像与线圈敏感度的方法：使用轻量、参数高效且可解释的混合高斯扩散模型作为图像先验，并对线圈敏感度施加经典光滑性先验。该方法在不同采样轨迹和对比度外分布数据下均表现稳健，性能接近传统变分惩罚如全变差（TV）方法，且实现快速推理。此外，概率框架支持计算后验期望与像素级方差，提供不确定性量化能力。
原文摘要 · Abstract (English)
Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters, restricting interpretability and increasing reconstruction time. Furthermore, parallel imaging reconstruction algorithms either rely on off-line coil sensitivity estimation, which is prone to misalignment and restricting sampling trajectories, or perform per-coil reconstruction, making the computational cost proportional to the number of coils. To overcome this, we jointly reconstruct the image and the coil sensitivities using the lightweight, parameter-efficient, and interpretable product of Gaussian mixture diffusion model as an image prior and a classical smoothness priors on the coil sensitivities. The proposed method delivers promising results while allowing for fast inference and demonstrating robustness to contrast out-of-distribution data and sampling trajectories, comparable to classical variational penalties such as total variation. Finally, the probabilistic formulation allows the calculation of the posterior expectation and pixel-wise variance.
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