Charles Epstein
University of Pennsylvania and the Flatiron Institute

“The Geometry of the Phase Retrieval Problem”

Abstract: In several imaging modalities the measured data can be interpreted as the modulus of the Fourier transform of a function describing the unknown object. To reconstruct this object one needs to use some auxiliary information to recover the un-measured phase of the Fourier transform. This is a notoriously difficult problem. I will discuss the underlying geometric reasons for these difficulties, approaches to improving the performance of standard algorithms, as well as entirely new approaches.


Biography: Prof. Epstein received his Ph.D. from NYU in 1983. He is a fellow of the American Association for the Advancement of Science. After three years as a postdoctoral fellow at Princeton University, he joined the faculty of the Department of Mathematics at the University of Pennsylvania, where he currently holds the Thomas A. Scott Chair in Mathematics. He has worked in spectral theory, hyperbolic geometry, univalent function theory, microlocal analysis, several complex variables and index theory. For more than a decade, he has also worked on a range of problems in medical imaging, image analysis, computational electromagnetics and mathematical aspects of population genetics. He was a Sloan Foundation Fellow in 1988–90. In 2007, he founded the Graduate Group in Applied Mathematics and Computational Science at the University of Pennsylvania, which he continues to chair.