Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Mona Zehni, Laurene Donati, Emmanuel Soubies, Zhizhen Zhao, Michael Unser

Research output: Contribution to journalArticlepeer-review


Single-particle cryo-electron microscopy (cryo-EM) reconstructs the three-dimensional (3D) structure of bio-molecules from a large set of 2D projection images with random and unknown orientations. A crucial step in the single-particle cryo-EM pipeline is 3D refinement, which resolves a high-resolution 3D structure from an initial approximate volume by refining the estimation of the orientation of each projection. In this work, we propose a new approach that refines the projection angles on the continuum. We formulate the optimization problem over the density map and the orientations jointly. The density map is updated using the efficient alternating-direction method of multipliers, while the orientations are updated through a semi-coordinate-wise gradient descent for which we provide an explicit derivation of the gradient. Our method eliminates the requirement for a fine discretization of the orientation space and does away with the classical but computationally expensive template-matching step. Numerical results demonstrate the feasibility and performance of our approach compared to several baselines.

Original languageEnglish (US)
Article number9052446
Pages (from-to)6151-6163
Number of pages13
JournalIEEE Transactions on Image Processing
StatePublished - 2020
Externally publishedYes


  • ADMM
  • Continuous angular refinement
  • Gradient descent
  • Joint reconstruction
  • Single-particle cryo-EM

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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