In single-particle cryo-electron microscopy (cryo-EM), the efficient
determination of orientation parameters for 2D projection images poses a
significant challenge yet is crucial for reconstructing 3D structures. This
task is complicated by the high noise levels present in the cryo-EM datasets,
which often include outliers, necessitating several time-consuming 2D clean-up
processes. Recently, solutions based on deep learning have emerged, offering a
more streamlined approach to the traditionally laborious task of orientation
estimation. These solutions often employ amortized inference, eliminating the
need to estimate parameters individually for each image. However, these methods
frequently overlook the presence of outliers and may not adequately concentrate
on the components used within the network. This paper introduces a novel
approach that uses a 10-dimensional feature vector to represent the orientation
and applies a Quadratically-Constrained Quadratic Program to derive the
predicted orientation as a unit quaternion, supplemented by an uncertainty
metric. Furthermore, we propose a unique loss function that considers the
pairwise distances between orientations, thereby enhancing the accuracy of our
method. Finally, we also comprehensively evaluate the design choices involved
in constructing the encoder network, a topic that has not received sufficient
attention in the literature. Our numerical analysis demonstrates that our
methodology effectively recovers orientations from 2D cryo-EM images in an
end-to-end manner. Importantly, the inclusion of uncertainty quantification
allows for direct clean-up of the dataset at the 3D level. Lastly, we package
our proposed methods into a user-friendly software suite named cryo-forum,
designed for easy accessibility by the developers.

一种基于深度学习的方法，使用 10 维特征向量表示方向，并应用二次约束二次规划推导出预测的方向作为单位四元数，附加不确定度指标，提出了一种考虑方向之间的成对距离的独特损失函数以提高方法的准确性，在文献中全面评估了编码器网络的设计选择。我们的数值分析证明了我们的方法在端到端的方式从 2D 冷冻电子显微镜图像中有效地恢复方向。重要的是，包括不确定度量化，允许在 3D 级别直接清理数据集。最后，我们将我们提出的方法打包到一个名为 cryo-forum 的开发者易于访问的软件套件中。