Compressive phase retrieval from squared output measurements via semidefinite programming

Henrik Ohlsson, Allen Y. Yang, Roy Dong, S. Shankar Sastry

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


Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, ℓ 1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a semidefinite program when the sampling rate is sufficiently high. This is an interesting finding since the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through extensive simulation and a practical experiment.

Original languageEnglish (US)
Title of host publicationSYSID 2012 - 16th IFAC Symposium on System Identification, Final Program
Number of pages6
EditionPART 1
StatePublished - 2012
Externally publishedYes
EventUniversite Libre de Bruxelles - Bruxelles, Belgium
Duration: Jul 11 2012Jul 13 2012

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


ConferenceUniversite Libre de Bruxelles


  • Compressive sensing
  • Phase retrieval
  • Semidefinite programming

ASJC Scopus subject areas

  • Control and Systems Engineering

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