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Performance of real phase retrieval

Abbasi, Ehsan and Salehi, Fariborz and Hassibi, Babak (2017) Performance of real phase retrieval. In: 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE , pp. 101-105. ISBN 978-1-5386-1565-2. https://resolver.caltech.edu/CaltechAUTHORS:20170908-075942456

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Abstract

This paper analyzes the mean-square error performance of the popular PhaseLift algorithm for phase retrieval, which is the problem of recovering an unknown signal from the magnitudes of a collection of linear measurements of the signal. This problem arises in many physical systems where only magnitudes can be measured. Our analysis approach is based on a novel comparison lemma, which upper bounds the performance of the convex-optimization-based PhaseLift algorithm in terms of an auxiliary convex optimization algorithm which is much more amenable to analysis. An upshot of our analysis is that an n-dimensional unknown signal can be recovered from the magnitudes of cn random linear measurements, where c > 1 is a constant (which empirically appears to be 3). This improves the best known earlier results which could only guarantee signal recovery with O(n log n) magnitude-only measurements. in fact, and more explicitly, we show that the sufficient number of the measurements in the high SNR regime (which corresponds to noiseless phase retrieval) can be derived from solving a deterministic convex optimization in 3 variables.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1109/SAMPTA.2017.8024478DOIArticle
http://ieeexplore.ieee.org/document/8024478/PublisherArticle
Additional Information:© 2017 IEEE. Date Added to IEEE Xplore: 04 September 2017.
Record Number:CaltechAUTHORS:20170908-075942456
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170908-075942456
Official Citation:E. Abbasi, F. Salehi and B. Hassibi, "Performance of real phase retrieval," 2017 International Conference on Sampling Theory and Applications (SampTA), Tallin, Estonia, 2017, pp. 101-105. doi: 10.1109/SAMPTA.2017.8024478
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81256
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:08 Sep 2017 18:30
Last Modified:03 Oct 2019 18:40

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