Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions


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Date

2024-02-15

Publication Type

Journal Article

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yes

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Abstract

It was recently shown that functions in L4([−B,B]) can be uniquely recovered up to a global phase factor from the absolute values of their Gabor transforms sampled on a rectangular lattice. We prove that this remains true if one replaces L4([−B,B]) by Lp([−B,B]) with p∈[1,∞]. To do so, we adapt the original proof by Grohs and Liehr and use a classical sampling result due to Beurling. Furthermore, we present a minor modification of a result of Müntz–Szász type by Zalik. Finally, we consider the implications of our results for more general function spaces obtained by applying the fractional Fourier transform to Lp([−B,B]) and for more general nonuniform sampling sets.

Publication status

published

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Book title

Volume

530 (2)

Pages / Article No.

127692

Publisher

Elsevier

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Edition / version

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Software

Geographic location

Date collected

Date created

Subject

Phase retrieval; Gabor transform; Sampling theory; Time-frequency analysis

Organisational unit

09603 - Alaifari, Rima (ehemalig) / Alaifari, Rima (former) check_circle

Notes

Funding

184698 - Mathematical analysis of the phase retrieval problem (SNF)

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