Clustering Tomographic Projections with the Earth Mover's Distance

Abstract

Classification and averaging tomographic projections of particles is an important step in the pipeline of single-particle cryo-electron microscopy. In this step, multiple noisy image patches taken of a single macromolecule from different viewing angles are clustered based on visual similarity and then averaged. The goal of this step is to provide clean images that can be used in downstream reconstruction tasks. Existing algorithms to cluster image patches rely on a rotationally invariant version of the L^2 distance. Although such algorithms have had some success at this task, the L^2 distance doesn't adequately capture the viewing angle difference between image patches. In this project we propose a new clustering algorithm based on a rotationally invariant Earth Mover's distance. We provide theoretical results detailing the relationship between the rotationally invariant Earth Mover's distance and the viewing angle difference between two image patches. Finally, we present simulations which demonstrate that our approach outperforms L^2-based clustering.