Inverse Problems, Imaging and Tensor Decomposition

Speaker: Joe Kileel

Location: Warren Weaver Hall 1314

Date: Feb. 12, 2020, 10 a.m.

Perspectives from computational algebra and non-convex 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.