Inverse Problems, Imaging and Tensor Decomposition

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

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