Phase Retrieval for L2([- π, π]) via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements

Mark Iwen, Michael Perlmutter, Nada Sissouno, Aditya Viswanathan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we focus on the approximation of smooth functions f: [- π, π] → C, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram) measurements. Two algorithms are developed for approximately inverting such measurements, each with theoretical error guarantees establishing their correctness. A detailed numerical study also demonstrates that both algorithms work well in practice and have good numerical convergence behavior.

Original languageEnglish
Article number8
JournalJournal of Fourier Analysis and Applications
Volume29
Issue number1
DOIs
StatePublished - Feb 2023

Keywords

  • Phase retrieval
  • Ptychography
  • Spectrogram measurements
  • STFT magnitude measurements
  • spectogram measurements

EGS Disciplines

  • Mathematics

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