© The Institution of Engineering and Technology
Compressed sensing (CS) has attracted considerable attention in signal processing because of its advantage of recovering sparse signals with lower sampling rates than the Nyquist rates. Greedy pursuit algorithms such as orthogonal matching pursuit (OMP) are well-known recovery algorithms in CS. In this study, the authors study a modified OMP proposed by Schnass et al., which uses a special sensing dictionary to identify the support of a sparse signal while maintaining the same computational complexity. The performance guarantee of this modified OMP in recovering the support of a sparse signal is analysed in the framework of mutual (cross) coherence. Furthermore, they discuss the modified OMP in the case of bounded noise and Gaussian noise, and show that the performance of the modified OMP in the presence of noise relies on the mutual (cross) coherence and the minimum magnitude of the non-zero elements of the sparse signal. Finally, simulations are constructed to demonstrate the performance of the modified OMP.
References
-
-
1)
-
D. Needell ,
J.A. Tropp
.
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples.
Appl. Comput. Harmon. Anal.
,
3 ,
301 -
321
-
2)
-
7. Wu, D., Zhu, W.P., Swamy, M.N.S.: ‘Compressive sensing-based speech enhancement in non-sparse noisy environments’, IET Signal Process., 2013, 7, (5), pp. 450–457 (doi: 10.1049/iet-spr.2012.0192).
-
3)
-
J.H.G. Ender
.
On compressive sensing applied to radar.
Elsevier Signal Process.
,
1402 -
1414
-
4)
-
16. Donoho, D.L., Elad, M., Temlyakov, V.N.: ‘Stable recovery of sparse overcomplete representations in the presence of noise’, IEEE Trans. Inf. Theory, 2006, 52, pp. 6–18 (doi: 10.1109/TIT.2005.860430).
-
5)
-
19. Elad, M.: ‘Sparse and redundant representations: from theory to applications in signal and imaging processing’ (Springer, New York, 2009).
-
6)
-
30. Tsaig, Y., Donoho, D.L.: ‘Extensions of compressed sensing’, Signal Process., 2006, 86, (3), pp. 549–571 (doi: 10.1016/j.sigpro.2005.05.029).
-
7)
-
20. Huang, A.M., Wan, Q., Yang, W.-L.: ‘Dictionary preconditioning for orthogonal matching pursuit in the presence of noise’. Int. Conf. on Communications, Circuits and Systems, 2009, pp. 419–422.
-
8)
-
13. Davenport, M.A., Wakin, M.B.: ‘Analysis of orthogonal matching pursuit using the restricted isometry property’, IEEE Trans. Inf. Theory, 2010, 56, (9), pp. 4395–4401 (doi: 10.1109/TIT.2010.2054653).
-
9)
-
D. Needell ,
R. Vershynin
.
Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit.
IEEE J. Sel. Top. Signal Process.
,
310 -
316
-
10)
-
10. Wang, J., Shim, B.: ‘On the recovery limit of sparse signals using orthogonal matching pursuit’, IEEE Trans. Signal Process., 2012, 60, (9), pp. 4973–4976 (doi: 10.1109/TSP.2012.2203124).
-
11)
-
8. Wu, R., Huang, W., Chen, D.: ‘The exact support recovery of sparse signals with noise via orthogonal matching pursuit’, IEEE Signal Process. Lett., 2013, 20, (4), pp. 403–406 (doi: 10.1109/LSP.2012.2233734).
-
12)
-
W. Dai ,
O. Milenkovic
.
Subspace pursuit for compressive sensing signal reconstruction.
IEEE Trans. Inf. Theory
,
5 ,
2230 -
2249
-
13)
-
D. Donoho
.
Compressed sensing.
IEEE Trans. Inf. Theory
,
2 ,
1289 -
1306
-
14)
-
12. Schnass, K., Vandergheynst, P.: ‘Dictionary preconditioning for greedy algorithms’, IEEE Trans. Signal Process., 2008, 56, (5), pp. 1994–2002 (doi: 10.1109/TSP.2007.911494).
-
15)
-
5. Majumdar, A., Ward, R.K.: ‘On the choice of compressed sensing priors and sparsifying transforms for MR image reconstruction: an experimental study’, Signal Process., 2012, 27, (9), pp. 1035–1048.
-
16)
-
10. Zhang, T.: ‘Sparse recovery with orthogonal matching pursuit under RIP’, IEEE Trans. Inf. Theory, 2011, 57, (9), pp. 6215–6221 (doi: 10.1109/TIT.2011.2162263).
-
17)
-
21. Li, B., Shen, Yi., Li, J.: ‘Dictionaries construction using alternating projection method in compressive sensing’, IEEE Signal Process. Lett., 2011, 18, (11), pp. 663–666 (doi: 10.1109/LSP.2011.2168517).
-
18)
-
25. Sharma, S.K., Patwary, M., Abdel-Maguid, M.: ‘Spectral efficient compressive transmission framework for wireless communication systems’, IET Signal Process., 2013, 7, (7), pp. 558–564 (doi: 10.1049/iet-spr.2012.0075).
-
19)
-
E. Candès ,
J. Romberg ,
T. Tao
.
Near-optimal signal recovery from random projections: universal encoding strategies?.
IEEE Trans. Inf. Theory
,
2 ,
489 -
509
-
20)
-
5. Cai, T.T., Wang, L.: ‘Orthogonal matching pursuit for sparse signal recovery with noise’, IEEE Trans. Inf. Theory, 2011, 57, (7), pp. 4680–4688 (doi: 10.1109/TIT.2011.2146090).
-
21)
-
J.A. Tropp
.
Greed is good: algorithmic results for sparse approximation.
IEEE Trans. Inf. Theory
,
10 ,
2231 -
2242
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2014.0164
Related content
content/journals/10.1049/iet-spr.2014.0164
pub_keyword,iet_inspecKeyword,pub_concept
6
6