Compressive phase retrieval

Matthew L. Moravec, Justin K. Romberg, Richard G. Baraniuk

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

122 Scopus citations


The theory of compressive sensing enables accurate and robust signal reconstruction from a number of measurements dictated by the signal's structure rather than its Fourier bandwidth. A key element of the theory is the role played by randomization. In particular, signals that are compressible in the time or space domain can be recovered from just a few randomly chosen Fourier coefficients. However, in some scenarios we can only observe the magnitude of the Fourier coefficients and not their phase. In this paper, we study the magnitude-only compressive sensing problem and in parallel with the existing theory derive sufficient conditions for accurate recovery. We also propose a new iterative recovery algorithm and study its performance. In the process, we develop a new algorithm for the phase retrieval problem that exploits a signal's compressibility rather than its support to recover it from Fourier transform magnitude measurements.

Original languageEnglish (US)
Title of host publicationWavelets XII
StatePublished - 2007
EventWavelets XII - San Diego, CA, United States
Duration: Aug 26 2007Aug 29 2007

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherWavelets XII
Country/TerritoryUnited States
CitySan Diego, CA


  • Compressive sensing
  • Phase retrieval
  • Projection algorithms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics


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