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CPRL: An Extension of Compressive Sensing to the Phase Retrieval Problem
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
University of California at Berkeley, USA.
University of California at Berkeley, USA.
University of California at Berkeley, USA.
2012 (English)In: Proceedings of the 26th Conference on Advances in Neural Information Processing Systems / [ed] P. Bartlett and F.C.N. Pereira and C.J.C. Burges and L. Bottou and K.Q. Weinberger, 2012, 1376-1384 p.Conference paper, Published paper (Refereed)
Abstract [en]

While compressive sensing (CS) has been one of the most vibrant research fields in the past few years, most development only applies to linear models. This limits its application in many areas where CS could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique – CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation. 

Place, publisher, year, edition, pages
2012. 1376-1384 p.
Keyword [en]
Phase retrieval, Compressive sensing, Compressive phase retrieval, X-ray crystallography, X-ray diffraction, Lifting, Sparse, Semidefinite programming
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-88925ISBN: 9781627480031 (print)OAI: oai:DiVA.org:liu-88925DiVA: diva2:606301
Conference
16th Conference on Advances in Neural Information Processing Systems, Lake Tahoe, NV, USA, 3-6 December, 2012
Projects
MOVIIICADICSLEARN
Funder
Linnaeus research environment CADICSEU, European Research Council, 267381
Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2013-07-10

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Ohlsson, Henrik

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CiteExportLink to record
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Citation style
  • apa
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  • sv-SE
  • Other locale
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Output format
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