A recovery algorithm is one of the most important components in compressive sensing. It is responsible for the recovery of sparse coefficients in some bases of the original signal from a set of non-adaptive and underdetermined linear measurements, and it is a key link between the front-end signal sensing system and back-end processing. In this study, an improved orthogonal matching pursuit algorithm based on singular value decomposition is proposed to overcome the limitations of existing algorithms, which effectively eliminates the correlation between the measured values. The results of simulation experiments show that the proposed algorithm significantly improves the average signal-to-noise ratio, and it performs more robustly than the classical orthogonal matching pursuit algorithm.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
E.J. Candès, J. Romberg, T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)
E.J. Candès, T. Tao, Near-optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)
E.J. Candès, J. Romberg, Sparsity and incoherence in compressive sampling. Inverse Prob. 23(3), 969–985 (2007)
E.J. Candès, The restricted isometry property and its implications for compressed sensing. C.R. Math. 346(9), 589–592 (2008)
E.J. Candès, M.B. Wakin, An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)
D.L. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
M.F. Duarte, M.A. Davenport, D. Takhar et al., Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag. 25(2), 83–91 (2008)
G.H. Golub, C.F. Van Loan, Matrix Computations (JHU Press, Baltimore, 2012)
M.A. Lexa, M.E. Davies, J.S. Thompson, Reconciling compressive sampling systems for spectrally sparse continuous-time signals. IEEE Trans. Signal Process. 60(1), 155–171 (2012)
J. Ma, G. Plonka, M.Y. Hussaini, Compressive video sampling with approximate message passing decoding. IEEE Trans. Circuits Syst. Video Technol. 22(9), 1354–1364 (2012)
D. Needell, R. Vershynin, Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Found. Comput. Math. 9(3), 317–334 (2009)
D. Needell, J.A. Tropp, CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)
J.A. Tropp, A.C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)
J.A. Tropp, Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004)
G. Xu, Z. Xu, Compressed sensing matrices from Fourier matrices. IEEE Trans. Inf. Theory 61(1), 469–478 (2015)
H.R. Yang, C. Zhang, D.W. Ding, Compressed sensing theory and reconstruction algorithm. Electron. J. 39(1), 142–148 (2011)
I thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Zhang, C. An Orthogonal Matching Pursuit Algorithm Based on Singular Value Decomposition. Circuits Syst Signal Process 39, 492–501 (2020) doi:10.1007/s00034-019-01182-2
- Compressive sensing
- Sparse prior
- Singular value decomposition
- Orthogonal matching pursuit algorithm