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Cryo-electron Microscopy01:28

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Conventional electron microscopy (EM) involves dehydration, fixation, and staining of biological samples, which distorts the native state of biological molecules and results in several artifacts. Also, the high-energy electron beam damages the sample and makes it difficult to obtain high-resolution images. These issues can be addressed using cryo-EM, which uses frozen samples and gentler electron beams. The technique was developed by Jacques Dubochet, Joachim Frank, and Richard Henderson, for...
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NON-UNIQUE GAMES OVER COMPACT GROUPS AND ORIENTATION ESTIMATION IN CRYO-EM.

Afonso S Bandeira1, Eth Zürich2, Yutong Chen3

  • 1Department of Mathematics, ETH Zürich Ramistrasse 101, 8092 Zürich, Switzerland.

Inverse Problems
|January 26, 2024
PubMed
Summary

We introduce a new convex relaxation for Non-Unique Games (NUG) using semidefinite programming (SDP). Our method improves rotation estimation accuracy in cryo-Electron Microscopy (cryo-EM) imaging, particularly at low signal-to-noise ratios (SNR).

Keywords:
Computer visionPrimary: 00A69Secondary: 90C34, 20C40algorithmscryo-EMoptimizationpattern recognition

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Area of Science:

  • Optimization
  • Applied Mathematics
  • Computational Imaging

Background:

  • The Non-Unique Games (NUG) problem seeks to minimize a function over a compact group.
  • Existing frameworks like the little Grothendieck problem and Unique Games are related.
  • NUG has applications in signal processing and computational biology, including cryo-EM.

Purpose of the Study:

  • To introduce a novel convex relaxation of the NUG problem using semidefinite programming (SDP).
  • To apply this SDP relaxation to the problem of orientation estimation in cryo-Electron Microscopy (cryo-EM).
  • To implement and evaluate an SDP solver for the NUG problem in cryo-EM.

Main Methods:

  • Convex relaxation of the NUG problem via Fourier transform and SDP.
  • Implementation of an SDP solver using the alternating direction method of multipliers (ADMM).
  • Numerical evaluation on synthetic datasets for cryo-EM orientation estimation.

Main Results:

  • The proposed SDP relaxation provides a generalized framework for NUG.
  • The ADMM-based solver demonstrates improved accuracy in estimating rotations for cryo-EM data.
  • Enhanced performance is observed particularly in low signal-to-noise ratio (SNR) conditions.

Conclusions:

  • The SDP relaxation offers a powerful approach to solving NUG problems.
  • The ADMM solver is a viable, albeit slower, method for accurate cryo-EM orientation estimation.
  • This work advances computational methods for analyzing cryo-EM data.