Algebraic constraints and algorithms for common lines in cryo-EM

Tommi Muller; Adriana L Duncan; Eric J Verbeke; Joe Kileel

doi:10.1017/S2633903X24000072

Algebraic constraints and algorithms for common lines in cryo-EM

Biol Imaging. 2024 May 16:4:e9. doi: 10.1017/S2633903X24000072. eCollection 2024.

Authors

Tommi Muller¹, Adriana L Duncan², Eric J Verbeke³, Joe Kileel^{2

4}

Affiliations

¹ Mathematical Institute, University of Oxford, Oxford, UK.
² Department of Mathematics, University of Texas at Austin, Austin, TX, USA.
³ Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.
⁴ Oden Institute, University of Texas at Austin, Austin, TX, USA.

Abstract

We revisit the topic of common lines between projection images in single-particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2n × n matrix storing properly scaled basis vectors for the common lines between n projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated with the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets.

Keywords: ADMM; common lines; cryo-electron microscopy; discrete heterogeneity; group synchronization; low-rank matrix.