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.
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published
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Volume
530 (2)
Pages / Article No.
127692
Publisher
Elsevier
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Subject
Phase retrieval; Gabor transform; Sampling theory; Time-frequency analysis
Organisational unit
09603 - Alaifari, Rima (ehemalig) / Alaifari, Rima (former)
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Funding
184698 - Mathematical analysis of the phase retrieval problem (SNF)
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