Information theoretic aspects of cryo-electron microscopy

Abstract

In the problem of single particle reconstruction in cryo-electron microscopy (cryo-EM), we want to recover the 3D electrostatic potential of a molecule from noisy 2D projections along unknown random viewing directions. A similar problem is multi-reference alignment (MRA), where we want to recover a signal from noisy circularly shifted copies, and the circular shifts are also unknown.

This thesis focuses on the sample complexity of these problems, that is, the number of observations required for signal estimation, as a function of the noise level, in the regime of large number of observations and high level of noise; this is the prevalent regime in cryo-EM. In this regime, the sample complexity is determined by the moments of the observations, thus we present various applications of the method of moments in MRA and cryo-EM.

Motivated by the tensor structure of higher order moments, we also develop a novel algorithm for symmetric even-order tensor decomposition.