Browse > Article

Generalized Orthogonal Matching Pursuit  

Kwon, Seok-Beop (School of Information and Communication, Korea University)
Shim, Byong-Hyo (School of Information and Communication, Korea University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SP / v.49, no.2, 2012 , pp. 122-129 More about this Journal
Abstract
As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we present an extension of OMP for pursuing efficiency of the index selection. Our approach, referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple (N) columns are identified per step. Using the restricted isometry property (RIP), we derive the condition for gOMP to recover the sparse signal exactly. The gOMP guarantees to reconstruct sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{NK}$ < $\frac{\sqrt{N}}{\sqrt{K}+2\sqrt{N}}$. In addition, we show recovery performance and the reduced number of iteration required to recover the sparse signal.
Keywords
orthogonal matching pursuit (OMP); compressive sensing (CS); restricted isometry property (RIP);
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. L. Donoho and P. B. Stark, "Uncertainty principles and signal recovery," SIAM Journal on Applied Mathematics, Vol. 49, no. 3, pp. 906-931, 1989.   DOI   ScienceOn
2 R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approximation, Vol. 28, no. 3, pp. 253-263, Dec. 2008.   DOI   ScienceOn
3 E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. on Information Theory, Vol. 52, no. 2, pp. 489-509, Feb. 2006.   DOI
4 E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. on Information Theory, Vol. 51, no. 12, pp. 4203-4215, Dec. 2005.   DOI   ScienceOn
5 R. Giryes and M. Elad, "RIP-Based Near-Oracle Performance Guarantees for SP, CoSaMP, and IHT," IEEE Trans. on Signal Processing, Vol. PP, no. 99, Nov. 2011.
6 J. A. Tropp and A. C. Gilbery, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. on Information Theory, Vol. 53, no. 12, pp. 4655-4666, Dec. 2007.   DOI
7 D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, Vol. 26, no. 3, pp. 301-321, Mar. 2009.   DOI   ScienceOn
8 W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. on Information Theory, Vol. 55, no. 5, pp. 2230-2249, May. 2009.   DOI
9 D. Needell and R. Vershynin, "Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," IEEE J. Sel. Topics Signal Processing, Vol. 4, no. 2, pp. 310-316, Apr. 2010.   DOI
10 D. L. Donoho and I. Drori and Y. Tsaig and J. L. Starck,, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," Mar. 2006.
11 M. A. Davenport and M. B. Wakin, "Analysis of Orthogonal Matching Pursuit using the restricted isometry property," IEEE Trans. on Information Theory, Vol. 56, no. 9, pp. 4395-4401, Sep. 2010.   DOI
12 E. J. Candes, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, Vol. 346, no. 9-10, pp. 589-592, May. 2008.   DOI   ScienceOn
13 J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. on Information Theory, Vol. 50, no. 10, pp. 2231-2242, Oct. 2004.   DOI   ScienceOn