用贝叶斯方法同时重建MRI图像并给出不确定性估计，更准确可靠。
Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models
- 基于稀疏先验的贝叶斯框架，结合梯度与小波变换建模图像
- 在多种采样模式下重建精度优于传统优化方法，且误差相关性高
- 适合需要可信图像质量评估的临床MRI场景
我们提出一种新颖的贝叶斯框架，用于从压缩感知磁共振成像数据中联合进行图像重建与不确定性量化。该问题被建模为线性逆问题，对未知图像参数赋予先验分布，假设图像在给定变换域中稀疏。我们构建了适用于任意稀疏化变换的通用框架，并在（1）基于图像空间梯度的总变差变换和（2）小波域变换上进行了验证。采用分裂-扩展吉布斯采样器进行贝叶斯推断，通过近端马尔可夫链蒙特卡洛方法高效采样非可微条件分布。所提算法在单线圈和多线圈数据集上，使用多种k空间采样模式与加速因子进行了验证。结果表明，该贝叶斯方法在图像重建性能上持续优于基于优化的方法，并能提供重建图像的不确定性估计。此外，估计的不确定性图与真实重建误差高度相关，显著优于基于深度学习的不确定性估计方法。
原文摘要 · Abstract (English)
We propose a novel Bayesian framework for joint image reconstruction and uncertainty quantification from compressed sensing magnetic resonance imaging data. The problem is formulated as a linear inverse problem, where prior distributions are assigned to the unknown image parameters. Specifically, the image is assumed to be sparse in a given transform domain. We develop a general framework applicable to any sparsifying transform and demonstrate its performance using (1) a total variation transform based on image spatial gradients and (2) a wavelet-domain transform. Bayesian inference is performed using a split-and-augmented Gibbs sampler, while the resulting non-differentiable conditional distributions are efficiently sampled using a proximal Markov chain Monte Carlo method. The proposed algorithms are validated on both single-coil and multi-coil datasets using various k-space sampling patterns and acceleration factors. The results demonstrate that the proposed Bayesian methods consistently outperform their optimisation-based counterparts in image reconstruction while providing uncertainty estimates for the reconstructed images. Furthermore, the estimated uncertainty maps show a strong correlation with the true reconstruction errors and substantially outperformed deep learning-based uncertainty estimation methods.
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