Convolutional Phase Retrieval

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish
Title of host publicationNIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems
EditorsUV Luxburg, I Guyon, S Bengio, H Wallach, R Fergus
Number of pages11
ISBN (Electronic)9781510860964
StatePublished - Dec 2017
Externally publishedYes
Event31st Conference on Neural Information Processing Systems - Long Beach Convention Center, Long Beach, United States
Duration: 4 Dec 20179 Dec 2017
Conference number: 31st

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference31st Conference on Neural Information Processing Systems
Abbreviated titleNIPS'17
Country/TerritoryUnited States
CityLong Beach


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