RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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

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

Citation in format AMSBIB
\Bibitem{Liv12} \by E.~D.~Livshits \paper On the efficiency of the Orthogonal Matching Pursuit in compressed sensing \jour Mat. Sb. \yr 2012 \vol 203 \issue 2 \pages 33--44 \mathnet{http://mi.mathnet.ru/msb7827} \crossref{https://doi.org/10.4213/sm7827} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2962611} \zmath{https://zbmath.org/?q=an:1259.94019} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012SbMat.203..183L} \elib{http://elibrary.ru/item.asp?id=19066416} \transl \jour Sb. Math. \yr 2012 \vol 203 \issue 2 \pages 183--195 \crossref{https://doi.org/10.1070/SM2012v203n02ABEH004218} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000302799500002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84859573445} 

• http://mi.mathnet.ru/eng/msb7827
• https://doi.org/10.4213/sm7827
• http://mi.mathnet.ru/eng/msb/v203/i2/p33

 SHARE:

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
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
3. E. D. Livshits, “On Uniform Approximation on Subsets”, Math. Notes, 98:5 (2015), 860–863
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
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
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
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
•  Number of views: This page: 481 Full text: 101 References: 70 First page: 28