Certain imaging applications such as x-ray crystallography require the recovery of a signal from magnitude-only measurements. This is a challenging inverse problem since the phase encapsulates a significant amount of structure in the underlying signal. In this talk, we discuss a recently introduced algorithm for solving the discrete phase retrieval problem from deterministic local measurements. Theoretical recovery guarantees as well as numerical results demonstrating the method's speed, accuracy and robustness will be provided.

This presentation is part of Minisymposium “MS49 - Image Restoration, Enhancement and Related Algorithms (4 parts)”
organized by: Weihong Guo (Case Western Reserve University) , Ke Chen (University of Liverpool) , Xue-Cheng Tai (Hong Kong Baptist University) , Guohui Song (Clarkson University) .

Authors:

Aditya Viswanathan (University of Michigan - Dearborn)

Brian Preskitt (University of California, San Diego)

Mark Iwen (Department of Mathematics, Michigan State University)

Rayan Saab (University of California, San Diego)

Keywords:

image reconstruction, inverse problems, nonlinear optimization, numerical linear algebra, phase retrieval, ptychography