MAXIMUM LIKELIHOOD FOR HIGH-NOISE GROUP ORBIT ESTIMATION AND SINGLE-PARTICLE CRYO-EM

• 成果类型: Article
• 署名作者: Fan, Zhou; Lederman, Roy R.; Sun, Yi; Wang, Tianhao; Xu, Sheng
• 署名单位: Yale University; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2292
• 发表日期: 2024
• 页码: 52-77
• 关键词: sample complexity; multireference alignment

摘要

Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the function domain. We describe a stratification of the Fisher information eigenvalues according to transcendence degrees of graded pieces of the algebra of group invariants, and we relate critical points of the loglikelihood landscape to a sequence of moment optimization problems, extending previous results for a discrete rotation group without projections. We then compute the transcendence degrees and forms of these optimization problems for several examples of function estimation under SO(2) and SO(3) rotations, including a simplified model of cryo-EM as introduced by resolve conjectures that third-order moments are sufficient to locally identify a generic signal up to its rotational orbit in these examples. For low-dimensional approximations of the electric potential maps of two small protein molecules, we empirically verify that the noise scalings of the Fisher information eigenvalues conform with our theoretical predictions over a range of SNR, in a model of SO(3) rotations without projections.