通过黎曼流形上基于测度的提升来正则化 Cryo-EM 三维图谱精修中的方向估计
Regularising orientation estimation in Cryo-EM 3D map refinement through measure-based lifting over Riemannian manifolds
AI总结：
本文提出椭球支撑提升（ESL）以正则化黎曼流形上的旋转估计，并将其融入 Cryo-EM 三维图谱与姿态联合重建的交替更新框架，证明适定性与误差界且实验显示旋转更接近真值。
摘要：
受单颗粒冷冻电子显微镜（Cryo-EM）中联合三维图谱重建与旋转估计在噪声鲁棒性和数据一致性之间权衡的启发，我们提出了椭球支撑提升（ESL），这是一种基于测度的提升方案，用于正则化并逼近黎曼流形上光滑函数的全局极小点。在关于极小点的唯一性假设下，我们证明了若干理论结果，特别是该方法的适定性，以及由所诱导偏置相对于全局极小点产生的误差界。此外，我们利用所发展的理论，将基于测度的提升方案整合到一种交替更新方法中，用于联合齐次三维图谱重建与旋转估计；在该问题中，通常需求解数万个流形取值的极小化问题，并且由于数据中的高噪声水平，正则化是必要的。通过使用 Cryo-EM 数据进行数值实验，该联合恢复方法被用于检验理论预测和算法性能。特别地，由 ESL 的正则化效应所诱导的偏置在经验上估计出比全局优化更好的旋转，即更接近真值的旋转。
英文摘要：
Motivated by the trade-off between noise-robustness and data-consistency for joint 3D map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularising and approximating the global minimiser of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimiser we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimiser. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimisation problems have to be solved and where regularisation is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularising effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimisation would.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
