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Inverse Problems, Imaging, and Tensor Decomposition

Applied Math and Analysis
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Friday, January 31, 2020
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12:00 pm - 1:00 pm
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Joe Kileel (Princeton)
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Applied Math And Analysis Seminar

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.