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Support Recovery from Noisy Measurement via Orthogonal Multi-Matching Pursuit

Published online by Cambridge University Press:  24 May 2016

Wei Dan
Wei Dan*
Affiliation:
School of Mathematics and Statistics, Guangdong University of Finance & Economics, Guangzhou 510320, China
*
*Corresponding author. Email address: [email protected] (W. Dan)
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Abstract

In this paper, a new stopping rule is proposed for orthogonal multi-matching pursuit (OMMP). We show that, for ℓ2 bounded noise case, OMMP with the new stopping rule can recover the true support of any K-sparse signal x from noisy measurements y = Фx + e in at most K iterations, provided that all the nonzero components of x and the elements of the matrix Ф satisfy certain requirements. The proposed method can improve the existing result. In particular, for the noiseless case, OMMP can exactly recover any K-sparse signal under the same RIP condition.

Keywords

65D1565J2268W40sparse recoveryorthogonal matching pursuitrestricted isometry property
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 2 , May 2016 , pp. 185 - 192
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Cai, T., and Wang, L., Orthogonal matching pursuit for sparse signal recovery with noise, IEEE Trans. Inf. Theory, vol. 57, no. 7 (2011), pp. 4680–4688.Google Scholar
[2]Candes, E. J., and Tao, T., Decoding by linear programming, IEEE Trans. Inf. Theory, vol. 51, no. 12 (2005), 4203–4215.Google Scholar
[3]Dai, W., and Milenkovic, O., Subspace pursuit for compressive sensing signal reconstruction, IEEE Trans. Inf. Theory, vol. 55, no. 5 (2009), pp. 2230–2249.Google Scholar
[4]Dan, W., Analysis of orthogonal multi-matching pursuit under restricted isometry property, Sci. China Math., vol. 57, no. 10 (2014), pp. 2179–2188.Google Scholar
[5]Dan, W., and Wang, R. H., Robustness of orthogonal matching pursuit under restricted isometry property, Sci. China Math., vol. 57, no. 3 (2014), pp. 627–634.Google Scholar
[6]Davenport, M. A., and Wakin, M. B., Analysis of orthogonal matching pursuit using the restricted isometry property, IEEE Trans. Inf. Theory, vol. 56, no. 9 (2010), pp. 4395–4401.Google Scholar
[7]Maleh, R., Improved RIP analysis of orthogonal matching pursuit, (2011), Arxiv: 1102.4311.Google Scholar
[8]Mallat, S., and Zhang, Z., Matching pursuit with time-frequency dictionaries, IEEE Trans. Signal Process., vol. 41, no. 12 (1993), pp. 3397–3415.Google Scholar
[9]Needell, D., and Tropp, J. A., CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Appl. Comput. Harm. Anal., vol. 26 (2009), pp. 301–321.Google Scholar
[10]Satpathi, S., Das, R., and Chakraborty, M., Improving the bound on the RIP constant in generalized orthogonal matching pursuit, IEEE Signal Process. Letters, vol. 20, no. 11 (2013), pp. 1074–1077.Google Scholar
[11]Tropp, J. A., Greed is good: Algorithmic results for sparse approximation, IEEE Trans. Inf. Theory, vol. 50, no. 10 (2004), pp. 2231–2242.Google Scholar
[12]Wang, J., Kwon, S., and Shim, B., Generalized orthogonal matching pursuit, IEEE Trans. Signal Process., vol. 60, no. 12 (2012), pp. 6202–6216.Google Scholar
[13]Wang, J., and Shim, B., Improved recovery bounds of orthogonal matching pursuit using restricted isometry property, (2012), Arxiv: 1211.4293.Google Scholar
[14]Xu, Z., The performance of orthogonal multi-matching pursuit under RIP, (2012), Arxiv: 1210.5323v2.Google Scholar