Convolutional Phase Retrieval

Qing Qu; Yuqian Zhang; Yonina C. Eldar; John Wright

doi:10.5555/3295222.3295357

Convolutional Phase Retrieval

Qing Qu, Yuqian Zhang, Yonina C. Eldar, John Wright

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study the convolutional phase retrieval problem, which considers recovery of an unknown signal x ∈ ℂn from m measurements consisting of the magnitudeofits cyclic convolution withaknown kernel a of lengthm. This model is motivated by applications to channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on byagiven channel/filter, and phase informationisdifficultorimpossible to acquire. We show that when a is random and m is sufficiently large, x can be efficiently recovered up to a global phase using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator; we overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis for alternating minimizing methods.

Original language	English
Title of host publication	NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems
Editors	UV Luxburg, I Guyon, S Bengio, H Wallach, R Fergus
Pages	6088–6098
Number of pages	11
ISBN (Electronic)	9781510860964
DOIs	https://doi.org/10.5555/3295222.3295357
State	Published - Dec 2017
Externally published	Yes
Event	31st Conference on Neural Information Processing Systems - Long Beach Convention Center, Long Beach, United States Duration: 4 Dec 2017 → 9 Dec 2017 Conference number: 31st

Publication series

Name	Advances in Neural Information Processing Systems
Volume	30
ISSN (Print)	1049-5258

Conference

Conference	31st Conference on Neural Information Processing Systems
Abbreviated title	NIPS'17
Country/Territory	United States
City	Long Beach
Period	4/12/17 → 9/12/17

Access to Document

10.5555/3295222.3295357License: Unspecified

https://dl.acm.org/doi/pdf/10.5555/3295222.3295357License: Unspecified

Cite this

Qu, Q., Zhang, Y., Eldar, Y. C., & Wright, J. (2017). Convolutional Phase Retrieval. In UV. Luxburg, I. Guyon, S. Bengio, H. Wallach, & R. Fergus (Eds.), NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems (pp. 6088–6098). (Advances in Neural Information Processing Systems; Vol. 30). https://doi.org/10.5555/3295222.3295357

@inproceedings{820f59681c184797a358793b314e9f07,

title = "Convolutional Phase Retrieval",

abstract = "We study the convolutional phase retrieval problem, which considers recovery of an unknown signal x ∈ ℂn from m measurements consisting of the magnitudeofits cyclic convolution withaknown kernel a of lengthm. This model is motivated by applications to channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on byagiven channel/filter, and phase informationisdifficultorimpossible to acquire. We show that when a is random and m is sufficiently large, x can be efficiently recovered up to a global phase using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator; we overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis for alternating minimizing methods.",

author = "Qing Qu and Yuqian Zhang and Eldar, {Yonina C.} and John Wright",

note = "This work was partially supported by the grants NSF CCF 1527809 and NSF IIS 1546411, the grants from the European Unions Horizon 2020 research and innovation program under grant agreement No. 646804-ERCCOGBNYQ, and the grant from the Israel Science Foundation under grant no. 335/14. QQ thanks the generous support of the Microsoft graduate research fellowship. We would like to thank Shan Zhong for the helpful discussion for real applications and providing the antenna data for experiments, and we thank Ju Sun and Han-wen Kuo for helpful discussion and input regarding the analysis of this work.; 31st Conference on Neural Information Processing Systems ; Conference date: 04-12-2017 Through 09-12-2017",

year = "2017",

month = dec,

doi = "10.5555/3295222.3295357",

language = "الإنجليزيّة",

series = "Advances in Neural Information Processing Systems",

pages = "6088–6098",

editor = "UV Luxburg and I Guyon and S Bengio and H Wallach and R Fergus",

booktitle = "NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems",

}

Qu, Q, Zhang, Y, Eldar, YC & Wright, J 2017, Convolutional Phase Retrieval. in UV Luxburg, I Guyon, S Bengio, H Wallach & R Fergus (eds), NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems. Advances in Neural Information Processing Systems, vol. 30, pp. 6088–6098, 31st Conference on Neural Information Processing Systems, Long Beach, California, United States, 4/12/17. https://doi.org/10.5555/3295222.3295357

Convolutional Phase Retrieval. / Qu, Qing; Zhang, Yuqian; Eldar, Yonina C. et al.
NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems. ed. / UV Luxburg; I Guyon; S Bengio; H Wallach; R Fergus. 2017. p. 6088–6098 (Advances in Neural Information Processing Systems; Vol. 30).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - We study the convolutional phase retrieval problem, which considers recovery of an unknown signal x ∈ ℂn from m measurements consisting of the magnitudeofits cyclic convolution withaknown kernel a of lengthm. This model is motivated by applications to channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on byagiven channel/filter, and phase informationisdifficultorimpossible to acquire. We show that when a is random and m is sufficiently large, x can be efficiently recovered up to a global phase using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator; we overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis for alternating minimizing methods.

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