Fast Phase Retrieval from Windowed Fourier Measurements via Wigner Distribution Deconvolution + Angular SynchronizationMS21

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) .

Mark Iwen (Department of Mathematics, Michigan State University)
Sami Merhi (Michigan State University)
Michael Perlmutter (Michigan State University)
fourier ptychography, image reconstruction, inverse problems, numerical linear algebra, phase retrieval, ptychography, stft measurements