Title: Mathematical challenges in cryo-electron microscopy

Abstract:

Cryo-electron microscopy (cryo-EM) is a method for determining the three-dimensional structures of molecules from images taken by an electron microscope. A central stage in the method is to determine a three-dimensional model of the molecule given only its 2D projection images. In particular, 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 will give a short introduction to cryo-EM and its related mathematical challenges. Then, we will focus on one of the stages in the reconstruction process and present a robust algorithm for determining the viewing directions of all cryo-EM images at once. 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 satisfies all pairwise relations.

No prior knowledge is required.

This is a joint work with Amit Singer from Princeton University.