Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, September 15, 2017
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Phase retrieval from local measurements

Abstract:   We consider an instance of the phase-retrieval problem, where one wishes to recover a signal (viewed as a vector) from the noisy magnitudes of its inner products with locally supported vectors. Such measurements arise, for example, in ptychography, which is an imaging technique used in lense-less X-ray microscopes and in optical microscopes with increased fields of view.

Starting with the setup where the signal is one-dimensional, we present theoretical and numerical results on an approach that has two important properties. First, it allows deterministic measurement constructions, which we give examples of. Second, it uses a robust, fast recovery algorithm that consists of solving a system of linear equations in a lifted space, followed by simply calculating an eigenvector. We also present a natural extension to the two-dimensional setting.

This is joint work with M. Iwen, B. Preskitts, and A. Viswanathan.

Files:


Speaker:  Rayan Saab
Institution:  University of California, San Diego

Event Organizer:   Martin Strauss    martinjs@umich.edu

 

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