In this paper, we reveal the formal algebraic structure underlying the intrinsic reconstitution algorithm, introduced by Singer and Shkolnisky in [9], for determining three dimensional macromolecular structures from images obtained by an electron microscope. Inspecting this algebraic structure, we obtain a conceptual explanation for the admissibility (correctness) of the algorithm and a proof of its numerical stability. In addition, we explain how the various numerical observations reported in that work follow from basic representation theoretic principles.

中文翻译：

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三维冷冻电子显微镜中的表征理论模式 I：内在重构算法

在本文中，我们揭示了由 Singer 和 Shkolnisky 在 [9] 中引入的内在重构算法的形式代数结构，用于从电子显微镜获得的图像中确定三维大分子结构。检查这种代数结构，我们获得了算法可接受性（正确性）的概念解释及其数值稳定性的证明。此外，我们解释了该工作中报告的各种数值观察结果如何遵循基本表示理论原则。