STFT Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms
Abstract
The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required in order to be able to uniquely, efficiently, and robustly identify the underlying signal. Inspired by practical methods in optical imaging, we consider the problem of signal reconstruction from the short-time Fourier transform (STFT) magnitude. We first develop conditions under, which the STFT magnitude is an almost surely unique signal representation. We then consider a semidefinite relaxation-based algorithm (STliFT) and provide recovery guarantees. Numerical simulations complement our theoretical analysis and provide directions for future work.
Additional Information
© 2015 IEEE. Manuscript received August 07, 2015; revised January 15, 2016; accepted March 15, 2016. Date of publication March 31, 2016; date of current version May 11, 2016. The work of K. Jaganathan and B. Hassibi was supported in part by the National Science Foundation under Grants CCF-0729203, CNS-0932428, and CIF-1018927, in part by the Office of Naval Research under the MURI Grant N00014-08-1-0747, and in part by a grant from Qualcomm Inc. and the work of Y. C. Eldar was supported in part by the European Union's Horizon 2020 Research and Innovation Program through the ERC-BNYQ Project, and in part by the Israel Science Foundation under Grant 335/14. The guest editor coordinating the review of this manuscript and approving it for publication was Prof. Justin Romberg. We would like to thank Mordechai Segev and Oren Cohen for introducing us to the STFT phase retrieval problem, and for many insightful discussions.Attached Files
Submitted - 1508.02820v3.pdf
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Additional details
- Eprint ID
- 67203
- Resolver ID
- CaltechAUTHORS:20160520-110029620
- NSF
- CCF-0729203
- NSF
- CNS-0932428
- NSF
- CIF-1018927
- Office of Naval Research (ONR)
- N00014-08-1-0747
- Qualcomm Inc.
- European Union Horizon 2020 Research and Innovation Program
- Israel Science Foundation
- 335/14
- Created
-
2016-05-20Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field