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Learning to recover orientations from projections in single-particle cryo-EM

Jelena Banjac, Laurène Donati, Michaël Defferrard.

A major challenge in single-particle cryo-electron microscopy (cryo-EM) is that the orientations adopted by the 3D particles prior to imaging are unknown; yet, this knowledge is essential for high-resolution reconstruction. We present a method to recover these orientations directly from the acquired set of 2D projections. Our approach consists of two steps: (i) the estimation of distances between pairs of projections, and (ii) the recovery of the orientation of each projection from these distances. In step (i), pairwise distances are estimated by a Siamese neural network trained on synthetic cryo-EM projections from resolved bio-structures. In step (ii), orientations are recovered by minimizing the difference between the distances estimated from the projections and the distances induced by the recovered orientations. We evaluated the method on synthetic cryo-EM datasets. Current results demonstrate that orientations can be accurately recovered from projections that are shifted and corrupted with a high level of noise. The accuracy of the recovery depends on the accuracy of the distance estimator. While not yet deployed in a real experimental setup, the proposed method offers a novel learning-based take on orientation recovery in SPA.

  title = {Learning to recover orientations from projections in single-particle cryo-EM},
  author = {Banjac, Jelena, Donati, Laur\`ene, and Defferrard, Micha\"el},
  year = {2021},
  url = {},


PDF available at arXiv:2104.06237, OpenReview:gwPPcc_M0lv.

Related: code, website.


Compile the latex source into a PDF with make. Run make clean to remove temporary files and make to prepare an archive to be uploaded on arXiv.


All the figures are in the figures folder. The code and data to reproduce them is found in the code repository.


The reviews, decision, and our answers are in and on OpenReview.


  • 2021-08-09: rebuttal to NeurIPS'21 reviews (git tag neurips-rebuttal)
  • 2021-06-04: submitted to NeurIPS'21 (git tag neurips-submitted)
  • 2021-04-13: uploaded on arXiv (git tag arxiv)


This work is licensed under a Creative Commons Attribution 4.0 International License.


Learning to recover orientations from projections in single-particle cryo-EM