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Complex phase retrieval from subgaussian measurements

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Krahmer, Felix ; Stöger, Dominik:
Complex phase retrieval from subgaussian measurements.
In: The journal of Fourier analysis and applications. 26 (20. November 2020) 6: 89. - 27 S.
ISSN 1069-5869 ; 1531-5851

Volltext

Open Access
Volltext Link zum Volltext (externe URL):
https://doi.org/10.1007/s00041-020-09797-9

Kurzfassung/Abstract

Phase retrieval refers to the problem of reconstructing an unknown vector x0∈Cn or x0∈Rn from m measurements of the form yi=∣∣⟨ξ(i),x0⟩∣∣2, where {ξ(i)}mi=1⊂Cm are known measurement vectors. While Gaussian measurements allow for recovery of arbitrary signals provided the number of measurements scales at least linearly in the number of dimensions, it has been shown that ambiguities may arise for certain other classes of measurements {ξ(i)}mi=1 such as Bernoulli measurements or Fourier measurements. In this paper, we will prove that even when a subgaussian vector ξ(i)∈Cm does not fulfill a small-ball probability assumption, the PhaseLift method is still able to reconstruct a large class of signals x0∈Rn from the measurements. This extends recent work by Krahmer and Liu from the real-valued to the complex-valued case. However, our proof strategy is quite different and we expect some of the new proof ideas to be useful in several other measurement scenarios as well. We then extend our results x0∈Cn up to an additional assumption which, as we show, is necessary.

Weitere Angaben

Publikationsform:Artikel
Schlagwörter:Phase retrieval; Small-ball method; Convex optimization; Descent cone analysis
Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Juniorprofessur für Data Science
Mathematisch-Geographische Fakultät > Mathematik > Mathematisches Institut für Maschinelles Lernen und Data Science (MIDS)
DOI / URN / ID:10.1007/s00041-020-09797-9
Open Access: Freie Zugänglichkeit des Volltexts?:Ja
Peer-Review-Journal:Ja
Verlag:Birkhäuser Boston
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Nein
KU.edoc-ID:29063
Eingestellt am: 02. Dez 2021 13:31
Letzte Änderung: 26. Sep 2024 12:12
URL zu dieser Anzeige: https://edoc.ku.de/id/eprint/29063/
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