3D ab initio modeling in cryo-EM by autocorrelation analysis

Eitan Levin, Tamir Bendory, Nicolas Boumal, Joe Kileel, Amit Singer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

23 Scopus citations


Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is the task of estimating the 3D structure of a molecule from a set of noisy 2D projections, taken from unknown viewing directions. Many algorithms for SPR start from an initial reference molecule, and alternate between refining the estimated viewing angles given the molecule, and refining the molecule given the viewing angles. This scheme is called iterative refinement. Reliance on an initial, user-chosen reference introduces model bias, and poor initialization can lead to slow convergence. Furthermore, since no ground truth is available for an unsolved molecule, it is difficult to validate the obtained results. This creates the need for high quality ab initio models that can be quickly obtained from experimental data with minimal priors, and which can also be used for validation. We propose a procedure to obtain such an ab initio model directly from raw data using Kam's autocorrelation method. Kam's method has been known since 1980, but it leads to an underdetermined system, with missing orthogonal matrices. Until now, this system has been solved only for special cases, such as highly symmetric molecules or molecules for which a homologous structure was already available. In this paper, we show that knowledge of just two clean projections is sufficient to guarantee a unique solution to the system. This system is solved by an optimization-based heuristic. For the first time, we are then able to obtain a low-resolution ab initio model of an asymmetric molecule directly from raw data, without 2D class averaging and without tilting. Numerical results are presented on both synthetic and experimental data.

Original languageEnglish (US)
Title of host publication2018 IEEE 15th International Symposium on Biomedical Imaging, ISBI 2018
PublisherIEEE Computer Society
Number of pages5
ISBN (Electronic)9781538636367
StatePublished - May 23 2018
Event15th IEEE International Symposium on Biomedical Imaging, ISBI 2018 - Washington, United States
Duration: Apr 4 2018Apr 7 2018

Publication series

NameProceedings - International Symposium on Biomedical Imaging
ISSN (Print)1945-7928
ISSN (Electronic)1945-8452


Other15th IEEE International Symposium on Biomedical Imaging, ISBI 2018
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging


  • Ab initio modeling
  • Autocorrelation analysis
  • Cryo-EM
  • Kam's method
  • Orthogonal matrix retrieval
  • Riemannian optimization
  • Single particle reconstruction


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