Improved recovery guarantees for phase retrieval from coded diffraction patterns

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex optimization. We provide recovery guarantees which require O(...

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Bibliographic Details
Published inApplied and computational harmonic analysis Vol. 42; no. 1; pp. 37 - 64
Main Authors Gross, D., Krahmer, F., Kueng, R.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2017
Subjects
Coded diffraction patterns
Compressed sensing
Golfing scheme
Low rank matrix recovery
Masked Fourier measurements
Phase retrieval
PhaseLift
Phase retrieval
Masked Fourier measurements
Golfing scheme
PhaseLift
Compressed sensing
Low rank matrix recovery
Coded diffraction patterns
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ISSN1063-5203
1096-603X
DOI10.1016/j.acha.2015.05.004

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Summary:In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex optimization. We provide recovery guarantees which require O(log2⁡d) different diffraction patterns, thus improving on recent results by Candès et al. [1], which demand O(log4⁡d) different patterns.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2015.05.004