Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sbornik: Mathematics, 2012, Volume 203, Issue 2, Pages 183–195
DOI: https://doi.org/10.1070/SM2012v203n02ABEH004218
(Mi sm7827)
 

This article is cited in 16 scientific papers (total in 16 papers)

On the efficiency of the Orthogonal Matching Pursuit in compressed sensing

E. D. Livshits

Evernote Corporation
References:
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.
Received: 03.12.2010 and 11.02.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 2, Pages 33–44
DOI: https://doi.org/10.4213/sm7827
Bibliographic databases:
Document Type: Article
UDC: 517.518.8
MSC: Primary 94A08, 94A11; Secondary 97N40, 46N40
Language: English
Original paper language: Russian
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/sm7827}
\crossref{https://doi.org/10.4213/sm7827}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2962611}
\zmath{https://zbmath.org/?q=an:1259.94019}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012SbMat.203..183L}
\elib{https://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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000302799500002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84859573445}
Linking options:
  • https://www.mathnet.ru/eng/sm7827
  • https://doi.org/10.1070/SM2012v203n02ABEH004218
  • https://www.mathnet.ru/eng/sm/v203/i2/p33
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:712
    Russian version PDF:284
    English version PDF:15
    References:107
    First page:28
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024