Variational Framework for Continuous Angular Refinement and Reconstruction in Cryo-EM
Mona Zehni, EPFL STI LIB

Meeting • 14 August 2018

Abstract
In the field of single particle reconstruction (SPR) in Cryo-electron microscopy (Cryo-EM), the target is to recover a high resolution density map of the molecule from a set of particle images. In this imaging modality, each particle image corresponds to the X-ray transform of the molecule from an unknown 3D pose corrupted by contrast transfer function (CTF) of the microscope and noise. In this presentation, we describe a variational framework that performs a joint optimization of the density map and the underlying angular variables. We solve this joint optimization problem by taking alternating ADMM and gradient descent steps to update the density map and 3D pose variables iteratively. Note that, our method serves as a 3D refinement step in the whole Cryo-EM pipeline. Thus, we start from an initial map and some rough estimations of the 3D poses and then refine both gradually. In our framework, unlike the current state of the art reconstruction techniques, we resolve the 3D pose variables on the continuum. Meaning that rather than descretizing the space of 3D poses, we represent these variables in their continuous form. This enables us to perform gradient steps on the angular variables in order to minimize the cost function. Thus, rather than comparing each particle image with a set of template projections of the density map taken from discretized points on the sphere, which is the essence of projection matching methods, we perform gradient steps in order to update these variables. Our preliminary results indicate that starting from a coarse estimation of the map and the angles, refinement of both is achievable.