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Maximum Likelihood for High-Noise Group Orbit Estimation and Cryo-EM

Abstract Number:

3814 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Sheng Xu (1), Zhou Fan (2), Tianhao Wang (3), Roy Lederman (4), Yi Sun (5)

Institutions:

(1) Princeton University, N/A, (2) N/A, N/A, (3) Yale University, N/A, (4) Yale University, New Haven, CT, (5) The University of Chicago, Chicago, IL

Co-Author(s):

Zhou Fan  
N/A
Tianhao Wang  
Yale University
Roy Lederman  
Yale University
Yi Sun  
The University of Chicago

First Author:

Sheng Xu  
Princeton University

Presenting Author:

Sheng Xu  
Princeton University

Abstract Text:

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.

Keywords:

Maximum Likelihood Estimation|Group Orbit Estimation|Fisher Information|Optimization Landscape|Moment Matching|Cryo-Electron Microscopy

Sponsors:

IMS

Tracks:

Statistical Theory

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