Codes and Expansions (CodEx) Seminar
Amit Singer (Princeton University)
Method of moments in cryo-electron microscopy
Over the past decade, single-particle cryo-EM has emerged as a leading method for elucidating macromolecular structures at near-atomic resolution, rivaling even the established technique of X-ray crystallography, while avoiding the crystallization bottleneck entirely. Cryo-EM was selected by the journal Nature Methods as Method of the Year 2015, the 2017 Nobel Prize in Chemistry was awarded to the pioneers of cryo-EM, and in the early days of the pandemic in 2020 cryo-EM was successfully used to image the SARS-CoV-2 spike protein. This talk will focus on the inverse problem of 3-D reconstruction in single-particle cryo-EM and solution approaches that are based on the method of moments. The method of moments provides insight into the sample complexity as a function of the noise level and involves just one pass over the data. However, it requires solving a large system of low-degree polynomial equations which in some cases imposes a computational challenge. We will provide an overview of recent results for cryo-EM as well as for the mathematical abstractions of multi-reference alignment and multi-target detection.