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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Numéro d'article	26
journal	Journal of Fourier Analysis and Applications
Volume	32
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00041-026-10234-6
état	Publié - 1 févr. 2026

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10.1007/s00041-026-10234-6

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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.",

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KW - Fourier transform

KW - disconnected support

KW - non-uniqueness

KW - phase retrieval problem

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On Non-uniqueness of Phase Retrieval in Multidimensions

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