A Representation Theory Perspective on Simultaneous Alignment and Classification
This addresses the challenge of 3D molecule reconstruction from noisy images with unknown orientations and sample heterogeneity, offering a more robust solution for Cryo-EM researchers, though it appears incremental as an extension of an existing framework.
The authors tackled the problem of simultaneous alignment and classification in heterogeneous Cryo-EM image analysis, which is prone to suboptimal local minima in existing methods, by extending the Non-Unique Games framework to provide a convex relaxation with certificates of global optimality under certain conditions.
One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule. Many algorithms for the reconstruction of molecules from images in heterogeneous Cryo-EM experiments are based on iterative approximations of the molecules in a non-convex optimization that is prone to reaching suboptimal local minima. Other algorithms require an alignment in order to perform classification, or vice versa. The recently introduced Non-Unique Games framework provides a representation theoretic approach to studying problems of alignment over compact groups, and offers convex relaxations for alignment problems which are formulated as semidefinite programs (SDPs) with certificates of global optimality under certain circumstances. In this manuscript, 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. Our proposed approach can also be extended to the case of continuous heterogeneity.