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

Area of Science:

• Computational Biology
• Structural Biology
• Information Theory

Background:

• Single-particle cryo-electron microscopy (cryo-EM) faces challenges with high noise and data rotation.
• Accurate function estimation is crucial for reconstructing molecular structures from cryo-EM data.

Purpose of the Study:

• To develop methods for function estimation in cryo-EM under high noise and rotational/projective transformations.
• To investigate the role of Fisher information and moment optimization in signal reconstruction.

Main Methods:

• Stratification of Fisher information eigenvalues using group invariants.
• Relating log-likelihood critical points to moment optimization problems.
• Analysis of SO(2) and SO(3) rotation groups, including a simplified cryo-EM model.

Main Results:

• Computed transcendence degrees and forms for moment optimization problems under SO(2) and SO(3) rotations.
• Affirmatively resolved conjectures regarding the sufficiency of 3rd-order moments for signal identification.
• Empirically verified theoretical predictions of Fisher information eigenvalue noise-scalings for protein potential maps.

Conclusions:

• The study provides theoretical and empirical validation for improved function estimation in cryo-EM.
• The findings contribute to a deeper understanding of information-theoretic limits in cryo-EM reconstruction.
• This work advances the analysis of noisy, rotationally invariant data in structural biology.