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 “recover” the un-measured phase of the Fourier transform. This is a notoriously difficult problem. I will discuss the underlying geometric reasons for this and approaches to improving the performance of standard algorithms.

Charles L. Epstein received his PhD in 1983 from NYU, and after a postdoc at Princeton, moved to Penn. Over the years he has worked in hyperbolic geometry, microlocal analysis, several complex variables, index theory, medical image analysis, MRI, population genetics, numerical analysis, and computational electromagnetics. He is a fellow of the AMS and the AAAS, and shared the Stefan Bergman prize with Francois Treves in 2016.