Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming

Key points

• \underset{g1,\ldots,gn\in \mathcal{G}}{\operatorname{min}}\,\, \frac{1}{|S|}\sum{i,j=1}^n \sum{s\in S} f{ij}(gi s gj^{-1}), \end{aligned} \] where $\mathcal{G}$ is a compact group, $S\subset \mathcal{G}$ is a finite subgroup of symmetry elements, and $f{ij}:\mathcal{G}\rightarrow \mathbb{R}$ is a loss function.1
• A notable example is common lines based orientation estimation of cryo-EM images for molecules with point group symmetry $S$, where $\mathcal{G}$ is the rotation group $\operatorname{SO}(3)$.1
• Unlike existing approaches which are tailored to specific symmetry groups, ours provides a unified computational framework for addressing all point group symmetries.1
• We demonstrate the applicability of the proposed algorithm on the cryo-EM orientation estimation problem on both simulated and experimental datasets.1

Sources (1)

• [1]Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 04:43 PM

  This paper extends the non-unique games framework introduced in Bandeira et al. (2020) to address symmetric structures.

  \underset{g_1,\ldots,g_n\in \mathcal{G}}{\operatorname{min}}\,\, \frac{1}{|S|}\sum_{i,j=1}^n \sum_{s\in S} f_{ij}(g_i s g_j^{-1}), \end{aligned} \] where $\mathcal{G}$ is a compact group, $S\subset \mathcal{G}$ is a finite subgroup of symmetry elements, and $f_{ij}:\mathcal{G}\rightarrow \mathbb{R}$ is a loss function.

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