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Mat. Sb., 2012, Volume 203, Number 2, Pages 33–44 (Mi msb7827)  

This article is cited in 7 scientific papers (total in 7 papers)

On the efficiency of the Orthogonal Matching Pursuit in compressed sensing

E. D. Livshits

Evernote Corporation

Abstract: The paper shows that if a matrix $\Phi$ has the restricted isometry property (RIP) of order $[CK^{1.2}]$ with isometry constant $\delta=cK^{-0.2}$ and if its coherence is less than $1/(20K^{0.8})$, then the Orthogonal Matching Pursuit (the Orthogonal Greedy Algorithm) is capable to exactly recover an arbitrary $K$-sparse signal from the compressed sensing $y=\Phi x$ in at most $[CK^{1.2}]$ iterations. As a result, an arbitrary $K$-sparse signal can be recovered by the Orthogonal Matching Pursuit from $M=O(K^{1.6}\log N)$ measurements.
Bibliography: 23 titles.

Keywords: Orthogonal Matching Pursuit, compressed sensing, coherence, restricted isometry property, sparsity.

DOI: https://doi.org/10.4213/sm7827

Full text: PDF file (499 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:2, 183–195

Bibliographic databases:

UDC: 517.518.8
MSC: Primary 94A08, 94A11; Secondary 97N40, 46N40
Received: 03.12.2010 and 11.02.2011

Citation: E. D. Livshits, “On the efficiency of the Orthogonal Matching Pursuit in compressed sensing”, Mat. Sb., 203:2 (2012), 33–44; Sb. Math., 203:2 (2012), 183–195

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Long Jingfan, Wei Xiujie, Ye Peixin, “Applications of Orthogonal Matching Pursuit in Compressed Sensing”, Proceedings of the International Conference on Computer, Networks and Communication Engineering (ICCNCE 2013), Advances in Intelligent Systems Research, 30, eds. Zheng D., Shi J., Zhang L., Atlantis Press, 2013, 13–16  mathscinet  isi
    2. Guodong Li, Linhua Huang, “Research on wavelet-based sparse representation of insulator leakage current signal”, Int. Trans. Electr. Energ. Syst., 25:1 (2015), 72–88  crossref  isi  scopus
    3. E. D. Livshits, “On Uniform Approximation on Subsets”, Math. Notes, 98:5 (2015), 860–863  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. J. Wang, S. Kwon, P. Li, B. Shim, “Recovery of sparse signals via generalized orthogonal matching pursuit: a new analysis”, IEEE Trans. Signal Process., 64:4 (2016), 1076–1089  crossref  mathscinet  isi  scopus
    5. J. Wang, B. Shim, Exact recovery of sparse signals using orthogonal matching pursuit: how many iterations do we need?, IEEE Trans. Signal Process., 64:16 (2016), 4194–4202  crossref  mathscinet  isi  scopus
    6. Aswathy G.P., Gopakumar K., “Wideband Spectrum Sensing Using Modulated Wideband Converter Byrevised Orthogonal Matching Pursuit”, 2018 International Conference on Control, Power, Communication and Computing Technologies (Iccpcct), IEEE, 2018, 179–184  isi
    7. Aswathy G.P., Gopakumar K., “Sub-Nyquist Wideband Spectrum Sensing Techniques For Cognitive Radio: a Review and Proposed Techniques”, AEU-Int. J. Electron. Commun., 104 (2019), 44–57  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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