Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction
This addresses the challenge of high noise in cryo-EM data for researchers in structural biology, but it is incremental as it builds on existing rotation-invariant features like the bispectrum.
The paper tackles the problem of heterogeneous multireference alignment for images, specifically for 2-D classification in cryo-EM, by proposing a framework that estimates target images directly from observations without clustering or registration, and demonstrates effectiveness on synthetic datasets.
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.