Maximum Likelihood and Moment Matching for High-Noise Group Orbit Estimation

Oregon Convention Center 

Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study a problem of group orbit estimation where samples of an unknown signal are observed under uniform random rotations from a rotational group. In high-noise regime, we describe a stratification of the Fisher information eigenvalues according to transcendence degrees in the algebra of group invariants. We relate the critical points of the log-likelihood optimization landscape to those of a sequence of moment matching problems. Some examples including a simplified model of cryo-EM will be discussed.

Maximum Likelihood Estimation

Group Orbit Estimation

Fisher Information

Optimization Landscape

Moment Matching

Cryo-Electron Microscopy 

IMS