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 approach, which involves searching for the orientation that maximizes cross-correlation relative to given templates, is sub-optimal, particularly under low signal-to-noise conditions. In this work, we propose a Bayesian framework for more accurate and flexible orientation estimation, with the minimum mean square error (MMSE) estimator serving as a key example. Through simulations, we demonstrate that the MMSE estimator consistently outperforms the cross-correlation-based method, especially in challenging low signal-to-noise scenarios, and we provide a theoretical framework that supports these improvements. When incorporated into iterative refinement algorithms in the 3D reconstruction pipeline, the MMSE estimator markedly improves reconstruction accuracy, reduces model bias, and enhances robustness to the ``Einstein from Noise'' artifact. Crucially, we demonstrate that orientation estimation accuracy has a decisive effect on downstream structural heterogeneity analysis. In particular, integrating the MMSE-based pose estimator into frameworks for continuous heterogeneity recovery yields accuracy improvements approaching those obtained with ground-truth poses, establishing MMSE-based pose estimation as a key enabler of high-fidelity conformational landscape reconstruction. 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：精确的取向估计是三维分子结构重建中的关键环节，无论是在单颗粒冷冻电子显微镜（cryo-EM）中，还是在日益流行的冷冻电子断层扫描（cryo-ET）领域。目前的主流方法是通过搜索使相对于给定模板的互相关最大化的取向，这种方法并非最优，尤其是在低信噪比条件下。在本工作中，我们提出了一个贝叶斯框架，用于实现更精确、更灵活的取向估计，其中最小均方误差（MMSE）估计器作为一个关键示例。通过模拟实验，我们证明了MMSE估计器在性能上持续优于基于互相关的方法，特别是在具有挑战性的低信噪比场景中，并且我们提供了一个支持这些改进的理论框架。当将MMSE估计器整合到三维重建流程的迭代优化算法中时，它能显著提高重建精度、减少模型偏差，并增强对“噪声中的爱因斯坦”伪影的鲁棒性。至关重要的是，我们证明了取向估计的准确性对下游结构异质性分析具有决定性影响。特别是，将基于MMSE的位姿估计器集成到连续异质性恢复框架中，所获得的精度提升接近于使用真实位姿得到的结果，这确立了基于MMSE的位姿估计是实现高保真构象景观重建的关键使能技术。这些发现表明，所提出的贝叶斯框架可以通过提高三维分子结构重建的准确性、鲁棒性和可靠性，从而显著推动冷冻电镜和冷冻电子断层扫描技术的发展，并促进对复杂生物系统的更深入理解。