Orientation determination of cryo-EM images using least unsquared deviations

Lanhui Wang, Amit Singer, Zaiwen Wen

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines-based methods estimate the orientations without additional geometric information. However, such methods fail when the detection rate of common-lines is too low due to the high level of noise in the images. An approximation to the least squares global self-consistency error was obtained in [A. Singer and Y. Shkolnisky, SIAM J. Imaging Sci., 4 (2011), pp. 543-572] using convex relaxation by semidefinite programming. In this paper we introduce a more robust global self-consistency error and show that the corresponding optimization problem can be solved via semidefinite relaxation. In order to prevent artificial clustering of the estimated viewing directions, we further introduce a spectral norm term that is added as a constraint or as a regularization term to the relaxed minimization problem. The resulting problems are solved using either the alternating direction method of multipliers or an iteratively reweighted least squares procedure. Numerical experiments with both simulated and real images demonstrate that the proposed methods significantly reduce the orientation estimation error when the detection rate of common-lines is low.

Original languageEnglish (US)
Pages (from-to)2450-2483
Number of pages34
JournalSIAM Journal on Imaging Sciences
Issue number4
StatePublished - Dec 3 2013

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics


  • Alternating direction method of multipliers
  • Angular reconstitution
  • Common-lines
  • Cryo-electron microscopy
  • Iteratively reweighted least squares
  • Least unsquared deviations
  • Semidefinite relaxation
  • Single particle reconstruction


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