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Transactions of the American Mathematical Society Series B

ISSN 2330-0000

   
 
 

 

Phase retrieval in infinite-dimensional Hilbert spaces


Authors: Jameson Cahill, Peter G. Casazza and Ingrid Daubechies
Journal: Trans. Amer. Math. Soc. Ser. B 3 (2016), 63-76
MSC (2010): Primary 46C05; Secondary 94A15
DOI: https://doi.org/10.1090/btran/12
Published electronically: October 6, 2016
MathSciNet review: 3554699
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Abstract: The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite-dimensional setting in which phase retrieval is always stable. This leads us to derive stability results for signals depending on how well they are approximated by finite expansions.


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Additional Information

Jameson Cahill
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
MR Author ID: 972323

Peter G. Casazza
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
MR Author ID: 45945

Ingrid Daubechies
Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708
MR Author ID: 54800
ORCID: 0000-0002-6472-1056

Received by editor(s): January 27, 2016
Received by editor(s) in revised form: June 21, 2016
Published electronically: October 6, 2016
Additional Notes: The second author was supported by NSF DMS 1609760; NSF ATD 1321779; and ARO W911NF-16-1-0008
The third author was supported by AFOSR grant 00002113-02; ONR grant N00014-11-1-0714-06-7; and NSF grant DMS-1516988
Article copyright: © Copyright 2016 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)