Robust phase retrieval algorithm for time-frequency structured measurements

Götz E. Pfander, Palina Salanevich

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This nonconvex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements taken with respect to a Gabor frame. It arises naturally in many practical applications, such as diffraction imaging and speech recognition. We present a reconstruction algorithm that uses a nearly optimal number of phaseless time-frequency structured measurements and discuss its robustness in the case when the measurements are corrupted by noise. We show how geometric properties of the measurement frame are related to the robustness of the phaseless reconstruction.

Original languageEnglish
Pages (from-to)736-761
Number of pages26
JournalSIAM Journal on Imaging Sciences
Volume12
Issue number2
DOIs
Publication statusPublished - 16 Apr 2019
Externally publishedYes

Funding

\ast Received by the editors August 6, 2018; accepted for publication (in revised form) February 7, 2019; published electronically April 16, 2019. http://www.siam.org/journals/siims/12-2/M120552.html Funding: The work of the second author was supported by a Research Grant for Doctoral Candidates and Young Academics and Scientists of German Academic Exchange Service (DAAD). \dagger Department of Scientific Computing, Catholic University of Eichst\a"tt-Ingolstadt, 85072 Germany (pfander@ku. de). \ddagger Department of Mathematics, University of California, Los Angeles, CA 90095-1555 ([email protected]).

Keywords

  • Angular synchronization
  • Expander graphs
  • Gabor frames
  • Order statistics of frame coefficients
  • Phase retrieval
  • Spectral clustering

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