Seminars & Colloquia Calendar
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.
