We will discuss phase retrieval from STFT magnitude measurements of a vector x based on a two step approach: First, a modified Wigner distribution deconvolution approach is used to solve for a portion of the lifted rank-one signal xx*. Second, an angular synchronization approach is used to recover x from the known portion of xx*. In addition to being computationally efficient the proposed method also gives insight into the design of good window/probe functions.

This presentation is part of Minisymposium “MS21 - Recent mathematical advances in phase retrieval and computational imaging (2 parts)”
organized by: Mahdi Soltanolkotabi (University of Southern California) , Tamir Bendory (Princeton University) .

Authors:

Mark Iwen (Department of Mathematics, Michigan State University)

Sami Merhi (Michigan State University)

Michael Perlmutter (Michigan State University)

Keywords:

fourier ptychography, image reconstruction, inverse problems, numerical linear algebra, phase retrieval, ptychography, stft measurements