On Non-uniqueness of Phase Retrieval in Multidimensions

Roman G. Novikov; Tianli Xu

doi:10.1007/s00041-026-10234-6

On Non-uniqueness of Phase Retrieval in Multidimensions

Roman G. Novikov
, Tianli Xu

IEPT RAS

Research output: Contribution to journal › Article › peer-review

Abstract

We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards complete description of non-uniqueness. Our examples include the case of functions with strongly disconnected compact support.

Original language	English
Article number	26
Journal	Journal of Fourier Analysis and Applications
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/s00041-026-10234-6
Publication status	Published - 1 Feb 2026

Keywords

Fourier transform
disconnected support
non-uniqueness
phase retrieval problem

Access to Document

10.1007/s00041-026-10234-6

Cite this

@article{b70f0f202dc547dc8a788d14c83473d2,

title = "On Non-uniqueness of Phase Retrieval in Multidimensions",

abstract = "We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on {"}oblique tensorization{"}, where one-dimensional results are strongly used, and its generalizations towards complete description of non-uniqueness. Our examples include the case of functions with strongly disconnected compact support.",

keywords = "Fourier transform, disconnected support, non-uniqueness, phase retrieval problem",

author = "Novikov, \{Roman G.\} and Tianli Xu",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.",

year = "2026",

month = feb,

day = "1",

doi = "10.1007/s00041-026-10234-6",

language = "English",

volume = "32",

journal = "Journal of Fourier Analysis and Applications",

issn = "1069-5869",

number = "1",

}

TY - JOUR

T1 - On Non-uniqueness of Phase Retrieval in Multidimensions

AU - Novikov, Roman G.

AU - Xu, Tianli

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

PY - 2026/2/1

Y1 - 2026/2/1

N2 - We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards complete description of non-uniqueness. Our examples include the case of functions with strongly disconnected compact support.

AB - We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards complete description of non-uniqueness. Our examples include the case of functions with strongly disconnected compact support.

KW - Fourier transform

KW - disconnected support

KW - non-uniqueness

KW - phase retrieval problem

UR - https://www.scopus.com/pages/publications/105029729679

U2 - 10.1007/s00041-026-10234-6

DO - 10.1007/s00041-026-10234-6

M3 - Article

AN - SCOPUS:105029729679

SN - 1069-5869

VL - 32

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 1

M1 - 26

ER -

On Non-uniqueness of Phase Retrieval in Multidimensions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this