Accurate orientation estimation is a crucial component of 3D molecular structure reconstruction, both in single-particle cryo-electron microscopy (cryo-EM) and in the increasingly popular field of cryo-electron tomography (cryo-ET). The dominant method, which involves searching for an orientation with maximum cross-correlation relative to given templates, falls short, particularly in low signal-to-noise environments. In this work, we propose a Bayesian framework to develop a more accurate and flexible orientation estimation approach, with the minimum mean square error (MMSE) estimator as a key example. This method effectively accommodates varying structural conformations and arbitrary rotational distributions. Through simulations, we demonstrate that our estimator consistently outperforms the cross-correlation-based method, especially in challenging conditions with low signal-to-noise ratios, and offer a theoretical framework to support these improvements. We further show that integrating our estimator into the iterative refinement in the 3D reconstruction pipeline markedly enhances overall accuracy, revealing substantial benefits across the algorithmic workflow. Finally, we show empirically that the proposed Bayesian approach enhances robustness against the ``Einstein from Noise'' phenomenon, reducing model bias and improving reconstruction reliability. These findings indicate that the proposed Bayesian framework could substantially advance cryo-EM and cryo-ET by enhancing the accuracy, robustness, and reliability of 3D molecular structure reconstruction, thereby facilitating deeper insights into complex biological systems.

翻译：在单颗粒冷冻电子显微镜（cryo-EM）以及日益流行的冷冻电子断层扫描（cryo-ET）领域中，精确的取向估计是三维分子结构重建的关键环节。目前的主流方法是通过搜索与给定模板具有最大互相关的取向来实现，但该方法存在不足，尤其在低信噪比环境下。本研究提出一个贝叶斯框架，以发展一种更精确、更灵活的取向估计方法，其中以最小均方误差（MMSE）估计器作为核心示例。该方法能有效适应不同的结构构象与任意旋转分布。通过仿真实验，我们证明该估计器在多种条件下均优于基于互相关的方法，尤其在低信噪比的挑战性环境中表现突出，并提供了支持这些改进的理论框架。我们进一步表明，将该估计器集成到三维重建流程的迭代精修中，能显著提升整体精度，在算法工作流的各个环节均体现出显著优势。最后，我们通过实验证明，所提出的贝叶斯方法增强了对“噪声中爱因斯坦”现象的鲁棒性，减少了模型偏差并提高了重建的可靠性。这些发现表明，所提出的贝叶斯框架可通过提升三维分子结构重建的精度、鲁棒性与可靠性，实质性推动冷冻电镜与冷冻电子断层扫描技术的发展，从而为深入理解复杂生物系统提供有力支持。