Department of Mathematics

Applied Mathematics

  •  Phase retrieval from local measurements
  •  09/14/2017
  •  4:10 PM - 5:00 PM
  •  C517 Wells Hall
  •  Rayan Saab, UCSD

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 li‰ed space, followed by fi€nding an eigenvector (e.g., via an inverse power iteration). ŒWe also present extensions to the two-dimensional setting. This is joint work with M. Iwen, B. Preskit, and A. Viswanathan.

 

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Michigan State University
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