The cryo-electron microscopy (cryo-EM) reconstruction problem is to find the three-dimensional structure of a macromolecule given noisy versions of its two-dimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryo-EM images of nearby viewing angles. This identification is an important first step in three-dimensional structure determination of macromolecules from cryo-EM, because once identified, these images can be rotationally aligned and averaged to produce "class averages" of better quality. The main advantage of our algorithm is its extreme robustness to noise. The algorithm is also very efficient in terms of running time and memory requirements, because it is based on the computation of the top few eigenvectors of a specially designed sparse Hermitian matrix. These advantages are demonstrated in numerous numerical experiments.

中文翻译：

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使用特征向量对冷冻电子显微镜图像进行视角分类。

冷冻电子显微镜 (cryo-EM) 重建问题是在给定未知随机方向的二维投影图像的噪声版本的情况下，找到大分子的三维结构。我们引入了一种新算法，用于识别附近视角的嘈杂冷冻电镜图像。这种识别是冷冻电镜大分子三维结构确定的重要第一步，因为一旦识别，这些图像可以旋转对齐并平均以产生更好质量的“类平均值”。我们算法的主要优点是它对噪声的极端鲁棒性。该算法在运行时间和内存要求方面也非常有效，因为它基于对专门设计的稀疏 Hermitian 矩阵的前几个特征向量的计算。