Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-29T04:38:35.574Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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