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 multireference alignment. The recent non-unique games framework provides a representation theoretic approach to alignment over compact groups, and offers a convex relaxation with certificates of global optimality in some cases. One of the great opportunities in cryo-EM is studying heterogeneous samples, containing two or more distinct 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 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 classes.

单粒子低温电子显微镜（EM）是一种从方向和位置随机且未知的单个大分子的许多嘈杂2D投影图像中确定大分子3D结构的方法。图像的方向分配问题是多参考对齐的动力所在。最近的非唯一游戏框架提供了一种表示理论方法来对紧凑的组进行对齐，并且在某些情况下提供了具有全局最优性证明的凸松弛。cryo-EM的巨大机遇之一是研究异质样品，其中包含两个或多个不同的分子构象。利用这一机会提出了算法挑战：确定每个粒子的类别和方向。