### Inverse Problems, Imaging and Tensor Decomposition

- Series
- Job Candidate Talk
- Time
- Tuesday, March 3, 2020 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Joe Kileel – Program in Applied and Computational Mathematics, Princeton University

Perspectives from numerical optimization and computational algebra are

brought to bear on a scientific application and a data science

application. In the first part of the talk, I will discuss

cryo-electron microscopy (cryo-EM), an imaging technique to determine

the 3-D shape of macromolecules from many noisy 2-D projections,

recognized by the 2017 Chemistry Nobel Prize. Mathematically, cryo-EM

presents a particularly rich inverse problem, with unknown

orientations, extreme noise, big data and conformational

heterogeneity. In particular, this motivates a general framework for

statistical estimation under compact group actions, connecting

information theory and group invariant theory. In the second part of

the talk, I will discuss tensor rank decomposition, a higher-order

variant of PCA broadly applicable in data science. A fast algorithm

is introduced and analyzed, combining ideas of Sylvester and the power

method.