IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Modern Optimization Meets Physics: Recent Progress on the Phase Retrieval Problem

  • April 24, 2015
  • 4 p.m.
  • LeConte 412

Abstract

In many imaging problems such as X-ray crystallography, detectors can only record the intensity or magnitude of a diffracted wave as opposed to measuring its phase. Phase retrieval concerns the recovery of an image from such phaseless information. Although this problem is in general combinatorially hard, it is of great importance because it arises in many applications ranging from astronomical imaging to speech analysis. This talk discusses novel acquisition strategies and novel convex and non-convex algorithms which are provably exact, thereby allowing perfect phase recovery from a minimal number of noiseless and intensity-only measurements. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. This may be of special contemporary interest because phase retrieval is at the center of spectacular current research efforts collectively known under the name of coherent diffraction imaging aimed, among other things, at determining the 3D structure of large protein complexes.

Brief Bio:
Emmanuel Candès is the Barnum-Simons Chair in Mathematics and Statistics, and professor of electrical engineering (by courtesy) at Stanford University. Up until 2009, he was the Ronald and Maxine Linde Professor of Applied and Computational Mathematics at the California Institute of Technology. His research interests are in applied mathematics, statistics, information theory, signal processing and mathematical optimization with applications to the imaging sciences, scientific computing and inverse problems. Candès graduated from the Ecole Polytechnique in 1993 with a degree in science and engineering, and received his Ph.D. in statistics from Stanford University in 1998. He has given over 60 plenary lectures at major international conferences including the International Congress of Mathematicians (2014). Emmanuel received the 2006 Alan T. Waterman Award from NSF, which recognizes the achievements of early-career scientists. Other honors include the 2013 Dannie Heineman Prize presented by the Academy of Sciences at Göttingen, the 2010 George Polya Prize awarded by the Society of Industrial and Applied Mathematics (SIAM), and the 2015 AMS-SIAM George David Birkhoff Prize in Applied Mathematics. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences.

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