http://iet.metastore.ingenta.com
1887

Detection of unknown and arbitrary sparse signals against noise

Detection of unknown and arbitrary sparse signals against noise

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Signal Processing — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The detection of sparse signals against background noise is difficult since the information in the signal is only carried by a small portion of it. Prior information is usually assumed to ease detection. This study considers the general unknown and arbitrary sparse signal detection problem when no prior information is available. Under a Neyman–Pearson hypothesis-testing problem model, a new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is proposed. The SE technique from the compressive sensing theory is incorporated into the LRT-SE to achieve the detection of sparse signals with unknown support sets and arbitrary non-zero entries. An analysis of the effectiveness of LRT-SE is first given in terms of the characterisation of the conditions for the Chernoff-consistent detection. A large deviation analysis is then given to characterise the error exponent of LRT-SE with respect to the signal-to-noise ratio and the angle between the sparse signal and its estimate. Numerical results demonstrate superior detection performance of the proposed scheme over existing asymptotically optimal sparse detectors for finite signal dimensions. In addition, the simulation shows that the error probability of the proposed scheme decays exponentially with the number of observations.

References

    1. 1)
      • 1. He, T., Ben-David, S., Tong, L.: ‘Nonparametric change detection in 2D random sensor field’. Proc. Int. Conf. Acoustics, Speech and Signal Processing, Philadelphia, PA, 2005, vol. 4, pp. 821824.
    2. 2)
      • 2. Liu, Y., Ning, P., Reiter, M.K.: ‘False data injection attacks against state estimation in electric power grids’. ACM Conf. Computer and Communications Security, Chicago, IL, 2009, pp. 2132.
    3. 3)
      • 3. Porat, B., Friedlander, B.: ‘Performance analysis of a class of transient detection algorithms-a unified framework’, IEEE Trans. Signal Process., 1992, 40, (10), pp. 25362546 (doi: 10.1109/78.157294).
    4. 4)
      • 4. Germida, A., Yan, Z., Plusquellic, J., Muradali, F.: ‘Defect detection using power supply transient signal analysis’. Int. Test Conf., Atlantic City, NJ, 1999, pp. 6776.
    5. 5)
      • 5. Learned, R., Willsky, A.: ‘A wavelet packet approach to transient signal classification’, Appl. Comput. Harmon. Anal., 1995, 2, (3), pp. 265278 (doi: 10.1006/acha.1995.1019).
    6. 6)
      • 6. Anderson, H., Gupta, M.: ‘Joint deconvolution and classification with applications to passive acoustic underwater multipath’, J. Acoust. Soc. Am., 2008, 124, (5), pp. 29732983 (doi: 10.1121/1.2981046).
    7. 7)
      • 7. Heger, A., Lappe, M., Holm, L.: ‘Accurate detection of very sparse sequence motifs’, J. Comput. Biol., 2004, 11, (5), pp. 843857 (doi: 10.1089/cmb.2004.11.843).
    8. 8)
      • 8. Lin, Y., Wu, Y., Hong, W., Zhang, B.: ‘Compressive sensing in radar imaging’. IET Int. Radar Conf., Guilin, China, 2009, pp. 13.
    9. 9)
      • 9. He, Y., Gu, X., Jian, T., Zhang, B., Li, B.: ‘A M out of N detector based on scattering density’. IET Int. Radar Conf., Guilin, China, 2009, pp. 14.
    10. 10)
      • 10. Ingster, Y.: ‘Minimax detection of a signal for ℓnp–balls’, Math. Meth. Stat., 1999, 7, pp. 401428.
    11. 11)
      • 11. Donoho, D., Jin, J.: ‘Higher criticism for detecting sparse heterogeneous mixtures’, Ann. Stat., 2004, 32, (3), pp. 962994 (doi: 10.1214/009053604000000265).
    12. 12)
      • 12. Trees, H.V.: ‘Detection, estimation, and modulation theory’ (John Wiley & Sons, New York, NY, 2001, 2nd edn.), Part I..
    13. 13)
      • 13. Kay, S.M.: ‘Fundamentals of statistical signal processing volume II: detection theory’ (Prentice-Hall PTR, Upper Saddle River, NJ, 1998, 1st edn.).
    14. 14)
      • 14. Zeitouni, O., Ziv, J., Merhav, N.: ‘When is the generalized likelihood ratio test optimal’, IEEE Trans. Inf. Theory, 1992, 38, pp. 15971602 (doi: 10.1109/18.149515).
    15. 15)
      • 15. Levy, B.C.: ‘Principles of signal detection and parameter estimation’ (Springer, New York, NY, 2008, 1st edn.).
    16. 16)
      • 16. Bickel, P.J., Chernoff, H.: ‘Asymptotic distribution of the likelihood ratio statistic in a prototypical nonregular problem’, in: Ghosh, J.K., Mitra, S.K., Parthasarathy, K.R., Prakasa Rao, B.L.S. (Eds.): ‘Statistics and probability: a Raghu RajBahadur Festschrift’ (Wiley Eastern, New Delhi, 1993) pp. 8396.
    17. 17)
      • 17. Hartigan, J.A.: ‘A failure of likelihood asymptotics for normal mixtures’. Le Cam, L.M., Olshen, R.A., (Eds.): Proc. Berkeley Conf. Honor of Jerzy Neyman and Jack Keifer (Eds), Wadsworth, Monterey, CA, 1985, vol. 2, pp. 807810.
    18. 18)
      • 18. Duarte, M.F., Davenport, M.A., Wakin, M.B., Baraniuk, R.G.: ‘Sparse signal detection from incoherent projections’. Proc. Int. Conf. Acoustics, Speech and Signal Processing, Toulouse, France, 2006, vol. 4, pp. 305308.
    19. 19)
      • 19. Davenport, M.A., Boufounos, P.T., Wakin, M.B., Baraniuk, R.G.: ‘Signal processing with compressive measurements’, IEEE J. Sel. Top. Signal Process., 2010, 4, (2), pp. 445460 (doi: 10.1109/JSTSP.2009.2039178).
    20. 20)
      • 20. Ben-Haim, Z., Eldar, Y., Elad, M.: ‘Coherence-based performance guarantees for estimating a sparse vector under random noise’, IEEE Trans. Signal Process., 2010, 58, (10), pp. 50305043 (doi: 10.1109/TSP.2010.2052460).
    21. 21)
      • 21. Candès, E., Romberg, J., Tao, T.: ‘Stable signal recovery from incomplete and inaccurate measurements’, Commun. Pure Appl. Math., 2006, LIX, pp. 12071233 (doi: 10.1002/cpa.20124).
    22. 22)
      • 22. Ben-Haim, Z., Eldar, Y., Elad, M.: ‘Coherence-based near-oracle performance guarantees for sparse estimation under Gaussian noise’. Proc. Int. Conf. Acoustics, Speech and Signal Processing, Dallas, TX, 2010, pp. 35903593.
    23. 23)
      • 23. Shao, J.: ‘Mathematical statistics’ (Springer-Verlag New York, New York, NY, 1999, 1st edn.).
    24. 24)
      • 24. Cover, T., Thomas, J.: ‘Elements of information theory’ (John Wiley & Sons, Hoboken, NJ, 2006, 2nd edn.).
    25. 25)
      • 25. Arias-Castro, E., Candès, E., Plan, Y.: ‘Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism’, Ann. Stat., 2011, 39, (5), pp. 25332556 (doi: 10.1214/11-AOS910).
    26. 26)
      • 26. Natarajan, B.K.: ‘Sparse approximation solutions to linear systems’, SIAM J. Comput., 1995, 24, (2), pp. 227234 (doi: 10.1137/S0097539792240406).
    27. 27)
      • 27. Boyd, S., Vanderberghe, L.: ‘Convex optimization’ (Cambridge Univ. Press, Cambridge, UK, 2004).
    28. 28)
      • 28. Candès, E., Tao, T.: ‘Decoding by linear programming’, IEEE Trans. Inf. Theory, 2005, 51, (12), pp. 42034210 (doi: 10.1109/TIT.2005.858979).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2011.0125
Loading

Related content

content/journals/10.1049/iet-spr.2011.0125
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address