SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

A Unified View of Schulz-Snyder Phase Retrieval Algorithm

Figen Oktem, Student of Professor Richard Blahut, University of Illinois

Date and Time: Dec 15, 2010 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Phase retrieval is the recovery of signals from Fourier transform magnitude with wide applications in crystallography, microscopy, optics, and astronomy. Although a unique solution almost always exists for two or higher dimensional signals, there is no known algorithm with guaranteed recovery. An iterative algorithm for recovering nonnegative real signals, based on minimizing the Csiszar's distance, was developed by Schulz and Snyder. We study the convergence properties of this algorithm from a unified viewpoint. We establish its relation to several well-known algorithms, including blind Richardson-Lucy, expectation-maximization, and alternating-minimization algorithms, and gradient-descent methods. These connections allow the algorithm to be seen in a new light, making many of its convergence properties, advantages and drawbacks almost obvious. The gained understanding yields new insights to improve the algorithm in terms of reliability and speed.