Skip to main content

Viewing Direction Estimation in Cryo-EM Using Synchronization

Author(s): Shkolnisky, Yoel; Singer, Amit

To refer to this page use:
Abstract: A central task in recovering the structure of a macromolecule from cryo-electron microscopy (cryo-EM) images is to determine a three-dimensional model of the macromolecule given many of its two-dimensional projection images. The direction from which each image was taken is unknown, and the images are small and extremely noisy. The goal is to determine the direction from which each image was taken and then to combine the images into a three-dimensional model of the molecule. We present an algorithm for determining the viewing direction of all cryo-EM images at once, which is robust to high levels of noise. The algorithm is based on formulating the problem as a synchronization problem; that is, we estimate the relative spatial configuration of pairs of images and then estimate a global assignment of orientations that maximizes the number of satisfied pairwise relations. Information about the spatial relation between pairs of images is extracted from common lines between triplets of images. These noisy pairwise relations are combined into a single consistent assignment of orientations by constructing a matrix whose entries encode the pairwise relations. This matrix is shown to have rank 3, and its nontrivial eigenspace is shown to reveal the projection orientation of each image. In particular, we show that the nontrivial eigenvectors encode the rotation matrix that corresponds to each image.
Publication Date: 2012
Electronic Publication Date: 20-Sep-2012
Citation: Shkolnisky, Yoel, Singer, Amit. (2012). Viewing Direction Estimation in Cryo-EM Using Synchronization. SIAM JOURNAL ON IMAGING SCIENCES, 5 (1088 - 1110. doi:10.1137/120863642
DOI: doi:10.1137/120863642
ISSN: 1936-4954
Pages: 1088 - 1110
Type of Material: Journal Article
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.