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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
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”, Sb. Math., 203:2 (2012), 183–195
Citation in format AMSBIB
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\by E.~D.~Livshits
\paper On the efficiency of the Orthogonal Matching Pursuit in compressed sensing
\jour Sb. Math.
\yr 2012
\vol 203
\issue 2
\pages 183--195
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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
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    Abstract page:721
    Russian version PDF:286
    English version PDF:17
    References:111
    First page:28
     
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