Heterogeneous multireference alignment for images with application to 2D classification in single particle reconstruction

Chao Ma, Tamir Bendory, Nicolas Boumal, Fred Sigworth, Amit Singer

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Motivated by the task of 2D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data.

Original languageEnglish (US)
Article number8864095
Pages (from-to)1699-1710
Number of pages12
JournalIEEE Transactions on Image Processing
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


  • Multireference alignment
  • bispectrum
  • cryo-EM
  • single particle reconstruction
  • steerable PCA


Dive into the research topics of 'Heterogeneous multireference alignment for images with application to 2D classification in single particle reconstruction'. Together they form a unique fingerprint.

Cite this