Abstract: Full-sampling Magnetic Resonance Imaging (MRI) requires a long scan time, which not only limits the detection efficiency but also tends to cause motion artifacts due to patient movement. To address the issues of high parameter sensitivity and inability to quantify uncertainty in traditional Compressed Sensing (CS) MRI reconstruction methods, a non-deterministic MRI reconstruction method named Bayesian Uncertainty-guided MRI (BU-MRI), based on wavelet-domain Sparse Bayesian Learning (SBL), was proposed. First, the advantage of wavelet transform in multi-resolution image representation was leveraged, and a hierarchical Bayesian probabilistic model was constructed by incorporating the sparsity of MRI images in the wavelet domain as a prior. Second, a posterior inference strategy combining Gibbs sampling and marginal likelihood maximization was adopted to achieve effective estimation of high-dimensional sparse coefficients and adaptive updating of hyperparameters. Third, based on the updated model parameters, high-quality images were iteratively recovered from the undersampled K-space data. Finally, pixel-wise posterior confidence intervals were also provided, offering a quantitative assessment of uncertainty for the reconstruction results. Validation using both simulated and real MRI data demonstrates that the method converges stably and exhibits good robustness under various sampling rates and noise levels. The experimental results show that the BU-MRI outperforms comparative methods such as Zero-Filled Inverse Discrete Fourier Transform (ZF-IDFT) and k-t Robust Principal Component Analysis (k-t RPCA) in terms of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). For example, at a sampling rate of 0.5, the reconstructed PSNR reaches 44.42 dB for cardiac MRI data and 40.37 dB for brain MRI data, with corresponding SSIM values of 0.9765 and 0.9547, respectively. These results outperform those obtained by ZF-IDFT and k-t RPCA. In the cardiac MRI data, for instance, ZF-IDFT and k-t RPCA yield PSNR values of only 39.92 dB and 38.72 dB, and SSIM values of 0.9518 and 0.9532, respectively.The proposed method performs excellently in structural fidelity, error suppression, and frequency-domain consistency, providing a reliable reconstruction framework with uncertainty quantification capability for clinical MRI.

Key words: Magnetic Resonance Imaging (MRI), Sparse Bayesian Learning (SBL), image reconstruction, wavelet transform, uncertainty quantification, Bayesian inference

摘要： 磁共振成像(MRI)全采样扫描时间长，既制约检测效率，还易因受检者移动产生运动伪影。针对传统压缩感知(CS)MRI重建方法参数敏感性高、无法量化结果不确定性的问题，提出一种基于小波域稀疏贝叶斯学习(SBL)的非确定性MRI重建方法(BU-MRI)。该方法首先利用小波变换对图像进行多分辨率表征的优势，通过刻画MRI图像在小波域中的稀疏性作为先验，构建一个分层贝叶斯概率模型。其次，采用吉布斯(Gibbs)采样与边际似然最大化相结合的后验推断策略，实现对高维稀疏系数的有效估计与超参数的自适应更新。再次，基于更新后的模型参数，从欠采样的K空间数据中迭代恢复出高质量图像。最后，该方法还能够输出像素级的后验置信区间，为重建结果提供定量化的不确定性评估。经仿真与真实MRI数据验证，该方法在不同采样率与噪声水平下收敛稳定且鲁棒性良好。仿真与真实MRI数据验证结果表明，BU-MRI在峰值信噪比(PSNR)与结构相似性指数(SSIM)指标上优于零填充逆离散傅里叶变换(ZF-IDFT)、k-t 鲁棒主成分分析(k-t RPCA)等方法；在真实心脏MRI数据和大脑MRI数据中，当采样率0.5时，重建数据的PSNR分别达到44.42 dB和40.37 dB，SSIM分别达到0.9765和0.9547，优于ZF-IDFT和k-t RPCA方法(在心脏MRI数据中，ZF-IDFT和k-t RPCA的PSNR分别达到39.92dB和38.72dB，SSIM分别达到0.9518和0.9532)。该方法在结构保真、误差抑制与频域一致性上表现优异，为临床MRI提供可靠且具备不确定性量化能力的重建框架。

关键词: 磁共振成像, 稀疏贝叶斯学习, 图像重建, 小波变换, 不确定性量化, 贝叶斯推断