Sparse phase retrieval from short-time fourier measurements

Yonina C. Eldar*, Pavel Sidorenko, Dustin G. Mixon, Shaby Barel, Oren Cohen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

76 Scopus citations

Abstract

We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform (STFT). We first show that the redundancy offered by the STFT enables unique recovery for arbitrary nonvanishing inputs, under mild conditions. An efficient algorithm for recovery of a sparse input from the STFT magnitude is then suggested, based on an adaptation of the recently proposed GESPAR algorithm. We demonstrate through simulations that using the STFT leads to improved performance over recovery from the oversampled Fourier magnitude with the same number of measurements.

Original languageEnglish
Article number6932437
Pages (from-to)638-642
Number of pages5
JournalIEEE Signal Processing Letters
Volume22
Issue number5
DOIs
StatePublished - 1 May 2015
Externally publishedYes

Keywords

  • GESPAR
  • phase retrieval
  • short-time Fourier transform
  • sparsity

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