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Notices of the American Mathematical Society.
Article . 2022 . Peer-reviewed
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Preprint . 2022
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https://dx.doi.org/10.48550/ar...
Article . 2022
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Preprint . 2022
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Algebraic Theory of Phase Retrieval

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2022Embargo end date: 01 Mar 2022 English Publisher:American Mathematical Society (AMS)Journal:Notices of the American Mathematical Society, volume 69 (issn: 0002-9920, eissn: 1088-9477, Copyright policy )
Authors: Tamir Bendory; Dan Edidin;

doi: 10.1090/noti2540 , 10.48550/arxiv.2203.02774

arXiv: 2203.02774

Algebraic Theory of Phase Retrieval

Abstract

We introduce five specific phase retrieval setups, present known results, and delineate open mathematical questions. We conclude by discussing the limitations of the algebraic point of view, and how other mathematical fields can provide indispensable insights into the phase retrieval problem.

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Keywords

Signal Processing (eess.SP), FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Physical sciences, Mathematical Physics (math-ph), Mathematics - Algebraic Geometry, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Electrical Engineering and Systems Science - Signal Processing, Algebraic Geometry (math.AG), Mathematical Physics

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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 8
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Top 10%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Top 10%
Average
Top 10%
Green
gold