SPARTA: Sparse phase retrieval via Truncated Amplitude flow

Gang Wang; Georgios B. Giannakis; Jie Chen; Mehmet Akcakaya

doi:10.1109/ICASSP.2017.7952902

SPARTA: Sparse phase retrieval via Truncated Amplitude flow

Gang Wang
, Georgios B. Giannakis
, Jie Chen
, Mehmet Akcakaya

Electrical and Computer Engineering

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

15 Scopus citations

Abstract

A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and, s2) a series of refinements by hard thresholding based truncated gradient iterations. SPARTA is simple, scalable, and fast. It recovers any k-sparse n-dimensional signal (k ≪ n) of large enough minimum (in modulus) nonzero entries from about k² log n measurements with high probability; this is achieved at computational complexity of order k²n log n, improving upon the state-of-the-art by at least a factor of k. SPARTA is robust against bounded additive noise. Simulated tests corroborate the merits of SPARTA relative to existing alternatives.

Original language	English (US)
Title of host publication	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3974-3978
Number of pages	5
ISBN (Electronic)	9781509041176
DOIs	https://doi.org/10.1109/ICASSP.2017.7952902
State	Published - Jun 16 2017
Event	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States Duration: Mar 5 2017 → Mar 9 2017

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)	1520-6149

Other

Other	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Country/Territory	United States
City	New Orleans
Period	3/5/17 → 3/9/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

Nonconvex optimization
hard thresholding
linear convergence
support recovery

Publisher link

10.1109/ICASSP.2017.7952902

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Wang, G., Giannakis, G. B., Chen, J., & Akcakaya, M. (2017). SPARTA: Sparse phase retrieval via Truncated Amplitude flow. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings (pp. 3974-3978). Article 7952902 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2017.7952902

SPARTA: Sparse phase retrieval via Truncated Amplitude flow. / Wang, Gang; Giannakis, Georgios B.; Chen, Jie et al.
2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. p. 3974-3978 7952902 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

Wang, G, Giannakis, GB, Chen, J & Akcakaya, M 2017, SPARTA: Sparse phase retrieval via Truncated Amplitude flow. in 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings., 7952902, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 3974-3978, 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017, New Orleans, United States, 3/5/17. https://doi.org/10.1109/ICASSP.2017.7952902

Wang G, Giannakis GB, Chen J, Akcakaya M. SPARTA: Sparse phase retrieval via Truncated Amplitude flow. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. p. 3974-3978. 7952902. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2017.7952902

Wang, Gang ; Giannakis, Georgios B. ; Chen, Jie et al. / SPARTA : Sparse phase retrieval via Truncated Amplitude flow. 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 3974-3978 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and, s2) a series of refinements by hard thresholding based truncated gradient iterations. SPARTA is simple, scalable, and fast. It recovers any k-sparse n-dimensional signal (k ≪ n) of large enough minimum (in modulus) nonzero entries from about k2 log n measurements with high probability; this is achieved at computational complexity of order k2n log n, improving upon the state-of-the-art by at least a factor of k. SPARTA is robust against bounded additive noise. Simulated tests corroborate the merits of SPARTA relative to existing alternatives.",

keywords = "Nonconvex optimization, hard thresholding, linear convergence, support recovery",

author = "Gang Wang and Giannakis, \{Georgios B.\} and Jie Chen and Mehmet Akcakaya",

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N2 - A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and, s2) a series of refinements by hard thresholding based truncated gradient iterations. SPARTA is simple, scalable, and fast. It recovers any k-sparse n-dimensional signal (k ≪ n) of large enough minimum (in modulus) nonzero entries from about k2 log n measurements with high probability; this is achieved at computational complexity of order k2n log n, improving upon the state-of-the-art by at least a factor of k. SPARTA is robust against bounded additive noise. Simulated tests corroborate the merits of SPARTA relative to existing alternatives.

AB - A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and, s2) a series of refinements by hard thresholding based truncated gradient iterations. SPARTA is simple, scalable, and fast. It recovers any k-sparse n-dimensional signal (k ≪ n) of large enough minimum (in modulus) nonzero entries from about k2 log n measurements with high probability; this is achieved at computational complexity of order k2n log n, improving upon the state-of-the-art by at least a factor of k. SPARTA is robust against bounded additive noise. Simulated tests corroborate the merits of SPARTA relative to existing alternatives.

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KW - hard thresholding

KW - linear convergence

KW - support recovery

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ER -

SPARTA: Sparse phase retrieval via Truncated Amplitude flow

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