Near-Optimal Bounds for Signal Recovery from Blind Phaseless Periodic Short-Time Fourier Transform

Tamir Bendory*, Chi yu Cheng, Dan Edidin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the problem of recovering a signal x∈ CN from samples of its phaseless periodic short-time Fourier transform (STFT): the magnitude of the Fourier transform of the signal multiplied by a sliding window w∈ CW. We show that if the window w is known, then a generic signal can be recovered, up to a global phase, from less than 4N phaseless STFT measurements. In the blind case, when the window is unknown, we show that the signal and the window can be determined simultaneously, up to a group of unavoidable ambiguities, from less than 4 N+ 2 W measurements. In both cases, our bounds are optimal, up to a constant smaller than two.

Original languageEnglish
Article number1
JournalJournal of Fourier Analysis and Applications
Volume29
Issue number1
DOIs
StatePublished - Feb 2023

Keywords

  • phase retrieval
  • ptychography
  • short-time Fourier transform

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