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

arXiv: https://arxiv.org/abs/1811.10382 · HTML: https://mlsanity.com/paper/1811.10382/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2018.

## Built on by (most cited first, 3 of 3)

- [An accelerated expectation-maximization algorithm for multi-reference alignment](https://mlsanity.com/paper/2105.07372/) (2021)
- [Unrolled algorithms for group synchronization](https://mlsanity.com/paper/2207.09418/) (2022)
- [Probabilistic PolarGMM: Unsupervised Cluster Learning of Very Noisy Projection Images of Unknown Pose](https://mlsanity.com/paper/2206.12959/) (2022)

## Abstract (arXiv)

Motivated by the task of 2-D 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.