EE Seminar: The generalized phase retrieval problem

(The talk will be given in English)

Speaker:     Prof. Dan Edidin

Mathematics, University of Missouri

Monday, April 28^th, 2025

13:00 - 14:00

The generalized phase retrieval problem

Abstract

The classical phase retrieval problem, which first arose in X-ray crystallography, is the problem of using prior information to estimate a signal from its Fourier magnitudes. The generalized phase retrieval problem entails using prior information to recover a collection of matrices from their Gram matrices. Mathematically, this problem arises from viewing phase retrieval through the lens of representation theory of compact groups. In classical phase retrieval the group is the circle group. When the group is the 3-dimensional rotation group we obtain applications to single-particle cryo-electron microscopy, a leading technique in structural biology. 

Short Bio

Dan Edidin is professor of mathematics at University of Missouri.  He received his undergraduate degree at Johns Hopkins University and his PhD from MIT, both in mathematics.  Before joining the faculty at Missouri, he was an NSF postdoctoral fellow at the University of Chicago. Dan’s original training was in algebraic geometry, which studies the solution sets of systems of multivariate polynomial equations. His early work was on problems that arise when a symmetry group acts on the system of equations. Dan's recent work has focused on using methods from algebraic geometry and representation theory to study problems at the foundations of two important experimental techniques in structural biology – X-ray crystallography and cryo electron-microscopy.

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