Lederman Roy R, Singer Amit
The Department of Statistics and Data Science, Yale University, New Haven, CT, USA.
The Department of Mathematics and the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.
Appl Comput Harmon Anal. 2020 Nov;49(3):1001-1024. doi: 10.1016/j.acha.2019.05.005. Epub 2019 Jun 5.
Single particle cryo-electron microscopy (EM) is a method for determining the 3-D structure of macromolecules from many noisy 2-D projection images of individual macromolecules whose orientations and positions are random and unknown. The problem of orientation assignment for the images motivated work on general multireference alignment. The recently introduced non-unique games framework provides a representation theoretic approach to alignment over compact groups, and offers a convex relaxation which is formulated as semidefinite programs with certificates of global optimality under certain circumstances. One of the great opportunities in cryo-EM is studying heterogeneous samples, containing two or more distinct classes or conformations of molecules. Taking advantage of this opportunity presents an algorithmic challenge: determining both the class and orientation of each particle. We generalize multireference alignment to a problem of alignment and classification, and we propose to extend non-unique games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying cryo-EM images and aligning them within their respective classes.
单颗粒冷冻电子显微镜（EM）是一种从单个大分子的许多有噪声的二维投影图像中确定大分子三维结构的方法，这些图像的方向和位置是随机且未知的。图像的方向分配问题推动了通用多参考对齐方面的工作。最近引入的非唯一博弈框架提供了一种在紧致群上进行对齐的表示理论方法，并提供了一种凸松弛，在某些情况下可将其表述为具有全局最优性证书的半定规划。冷冻电子显微镜的重大机遇之一是研究包含两种或更多不同分子类别或构象的异质样本。利用这一机遇带来了算法挑战：确定每个颗粒的类别和方向。我们将多参考对齐推广到对齐和分类问题，并提议将非唯一博弈扩展到同时对齐和分类问题，目标是同时对冷冻电子显微镜图像进行分类并在各自类别内进行对齐。
