Joe Kileel : Inverse Problems, Imaging, and Tensor Decomposition (Jan 31, 2020 11:55 AM)

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 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.

• Category: Applied Math and Analysis
• Duration: 01:34:45
• Date:  January 31, 2020 at 11:55 AM
• Views: 374
• Tags:   seminar, Applied Math And Analysis Seminar