Fast compressive phase retrieval from Fourier measurements

Çagkan Yapar; Volker Pohl; Holger Boche

ICASSP 2015accepted0 citations

Fast compressive phase retrieval from Fourier measurements

Abstract

This paper considers the problem of recovering a k-sparse, N-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very high probability whenever M ≳ 4k log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (N/k) random Fourier intensity measurements are available. The proposed algorithm is comprised of two stages: An algebraic phase retrieval stage and a compressive sensing step subsequent to it. Simulation results are provided to demonstrate the applicability of the algorithm for noiseless and noisy scenarios.

BibTeX

@inproceedings{icassp2015_fastcompressivep,
  title = {Fast compressive phase retrieval from Fourier measurements},
  author = {Çagkan Yapar and Volker Pohl and Holger Boche},
  booktitle = {ICASSP 2015},
  year = {2015}
}