Singer A, Zhao Z, Shkolnisky Y, Hadani R
Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000 (
SIAM J Imaging Sci. 2011 Jun 23;4(2):723-759. doi: 10.1137/090778390.
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.
冷冻电子显微镜（cryo-EM）重建问题是在给定未知随机方向上其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来识别相近视角下的有噪声冷冻电子显微镜图像。这种识别是从冷冻电子显微镜确定大分子三维结构的重要第一步，因为一旦识别出来，这些图像就可以进行旋转对齐和平均，以产生质量更好的“类平均图像”。我们算法的主要优点是对噪声具有极强的鲁棒性。该算法在运行时间和内存需求方面也非常高效，因为它基于对一个特别设计的稀疏埃尔米特矩阵的前几个特征向量的计算。这些优点在大量数值实验中得到了证明。
