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：在单颗粒冷冻电子显微镜（cryo-EM）及日益流行的冷冻电子断层扫描（cryo-ET）技术中，精确的取向估计是三维分子结构重建的关键环节。目前主流方法通过搜索与给定模板互相关最大化的取向进行估计，该方法并非最优，尤其在低信噪比条件下表现欠佳。本研究提出一种贝叶斯框架，旨在实现更精确、更灵活的取向估计，其中最小均方误差（MMSE）估计器作为核心示例。通过仿真实验，我们证明MMSE估计器在各类场景下均优于基于互相关的方法，尤其在具有挑战性的低信噪比条件下优势显著，并提供了支撑该改进的理论框架。当将MMSE估计器集成至三维重建流程的迭代优化算法时，其显著提升了重建精度、降低了模型偏差，并增强了对“噪声爱因斯坦”伪影的鲁棒性。关键的是，我们证明了取向估计精度对下游结构异质性分析具有决定性影响。特别地，将基于MMSE的位姿估计器整合至连续异质性恢复框架中，所获得的精度提升接近使用真实位姿数据的效果，这确立了基于MMSE的位姿估计作为实现高保真构象景观重建的关键技术。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，显著推动冷冻电镜与冷冻电子断层扫描技术的发展，从而为深入解析复杂生物系统提供有力支撑。