三维低温电子显微术多频类平均的表示论模式
Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron Microscopy
摘要：
我们在本文中开发了一种新的内在分类算法-多频类平均（MFCA）-分类噪声投影图像从三维冷冻电子显微镜（cryo-EM）之间的相似性，他们的观察方向。这种新算法利用酉群的多个不可约表示将额外的冗余引入到最优平面内旋转对准的表示中，扩展并优于仅使用单个表示的现有类平均算法。所提出的MFCA算法的形式代数模型和表示理论模式将Hadani和Singer的框架扩展到酉群的任意不可约表示。通过Wigner $D$ -矩阵的透镜，考察了广义局域平行输运算子的谱性质，在概念上建立了MFCA的一致性和稳定性.我们证明了所提出的算法的有效性与数值实验。
英文摘要：
We develop in this paper a novel intrinsic classification algorithm -- multi-frequency class averaging (MFCA) -- for classifying noisy projection images obtained from three-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing directions. This new algorithm leverages multiple irreducible representations of the unitary group to introduce additional redundancy into the representation of the optimal in-plane rotational alignment, extending and outperforming the existing class averaging algorithm that uses only a single representation. The formal algebraic model and representation theoretic patterns of the proposed MFCA algorithm extend the framework of Hadani and Singer to arbitrary irreducible representations of the unitary group. We conceptually establish the consistency and stability of MFCA by inspecting the spectral properties of a generalized local parallel transport operator through the lens of Wigner $D$-matrices. We demonstrate the efficacy of the proposed algorithm with numerical experiments.
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