Organizing Committee
  • Bernhard Bodmann
    University of Houston
  • Jian-Feng Cai
    The Hong Kong University of Science and Technology
  • Peter Casazza
    University of Missouri
  • Yang Wang
    The Hong Kong University of Science and Technology
Abstract

This program will focus on phase retrieval, a research area introduced by Pete Casazza (one of the organizers of this program) and others. Phase retrieval originates from harmonic analysis, where one wants to recover a function from the magnitude of its Fourier transform without any phase information. The phase retrieval problem has a natural generalization to finite dimensional Hilbert spaces. A finite dimensional signal is sought to fit the magnitudes of its linear measurements. Phase retrieval in this finite dimensional setting has become one of the growing research areas in recent years. The techniques from the finite dimensional setting are promising to become indispensable in many imaging techniques such as x-ray crystallography, electron microscopy, diffractive imaging, astronomical imaging, x-ray tomography etc. It also has other important applications in optics, communication, audio signal processing, and more.

Many challenging and fundamental problems in phase retrieval remain open. For example, it is still unknown what is the minimal number of measurements needed for any d-dimensional signal is phase retrievable. A challenging problem of very practical importance is the computational efficiency of phase retrieval algorithms. So far the existing phase retrieval algorithms can be loosely divided into three categories: (a) Using a very large number of measurements N, in the order of N>=O(d^2); (b) Convex relaxation algorithms using random measurements, and (c) Constructing special measurements that allow fast and robust phase retrievals.

The program will bring a group of researchers from the US and HKUST with common interests and complementary expertise to work intensely on new theory, applications and algorithms for phase retrieval.