Sparse phase retrieval via iteratively reweighted amplitude flow

Gang Wang, Liang Zhang, Georgios B. Giannakis, Jie Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Sparse phase retrieval (PR) aims at reconstructing a sparse signal vector from a few phaseless linear measurements. It emerges naturally in diverse applications, but it is NP-hard in general. Drawing from advances in nonconvex optimization, this paper presents a new algorithm that is termed compressive reweighted amplitude flow (CRAF) for sparse PR. CRAF operates in two stages: Stage one computes an initial guess by means of a new spectral procedure, and stage two implements a few hard thresholding based iteratively reweighted gradient iterations on the amplitude-based least-squares cost. When there are sufficient measurements, CRAF reconstructs the true signal vector exactly under suitable conditions. Furthermore, its sample complexity coincides with that of the state-of-the-art approaches. Numerical experiments showcase improved performance of the proposed approach relative to existing alternatives.

Original languageEnglish (US)
Title of host publication2018 26th European Signal Processing Conference, EUSIPCO 2018
PublisherEuropean Signal Processing Conference, EUSIPCO
Number of pages5
ISBN (Electronic)9789082797015
StatePublished - Nov 29 2018
Event26th European Signal Processing Conference, EUSIPCO 2018 - Rome, Italy
Duration: Sep 3 2018Sep 7 2018

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491


Other26th European Signal Processing Conference, EUSIPCO 2018


  • Linear convergence
  • Model-based hard thresholding
  • Sparse recovery
  • Spectral initialization


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