Past Event:
Inverse Problems and Imaging
Joe Kileel, Postdoctoral Fellow, Program in Applied and Computational Mathematics, Princeton University
1:30 – 3PM
Tuesday Jan 21, 2020
POB 6.304
Abstract
Cryo-electron microscopy (cryo-EM) is an imaging technique to determine the shape of 3-D macromolecules from massive datasets of noisy 2-D projections. Recognized by the 2017 Chemistry Nobel Prize, cryo-EM captures molecules in their native states, in contrast to traditional imaging modalities. The tradeoff is that the resulting inverse problem has rich mathematical and computational challenges, including extreme noise, unknown orientations, big data and conformational heterogeneity.
This lecture presents computational mathematics that has arisen from cryo-EM. In particular, I will discuss a general framework for
estimation under compact group actions, that connects information theory and group invariant theory. Other perspectives from
computational algebra also appear, including robust solvers for certain large-scale polynomial systems and fast methods for tensor
rank decomposition. These ideas are brought together in a moment-based approach for ab initio cryo-EM reconstruction, in which the computational complexity is controlled mostly by the desired resolution rather than the size of the dataset.