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Applied and Computational Math Seminar

Inverse Problems, Imaging and Tensor Decomposition

Joe Kileel, Princeton University

Location:  Room 705
Date & time: Monday, 27 January 2020 at 2:00PM - 3:00PM

Abstract:
Perspectives from computational algebra and numerical optimization 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 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.