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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm7827https://doi.org/10.1070/SM2012v203n02ABEH004218 https://www.mathnet.ru/eng/sm/v203/i2/p33
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Abstract page: | 712 | Russian version PDF: | 284 | English version PDF: | 15 | References: | 107 | First page: | 28 |
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