Advertisement

Neural Processing Letters

, Volume 50, Issue 3, pp 2389–2406 | Cite as

A Novel Noise-Enhanced Back-Propagation Technique for Weak Signal Detection in Neyman–Pearson Framework

  • Sumit KumarEmail author
  • Ayush Kumar
  • Rajib Kumar Jha
Article
  • 105 Downloads

Abstract

In this paper, we propose a noise enhanced neural network based detector. The proposed method can detect the known weak signal in additive non-Gaussian noise. Carefully injected noise in a neural network enhances the weak signal detection performance. During training, the back-propagation algorithm achieves less error and it converges faster with the addition of the external noise. The optimum value of external noise is calculated theoretically and justified by simulation. This method excels over the traditional neural network based detectors in terms of its performance characteristics i.e., the probability of detection (\(P_D\)) at some specified probability of false alarm (\(P_{FA}\)). Performance of the noise enhanced neural network based detector under several signal-to-noise ratio environments are also compared with state-of-the-art detectors.

Keywords

Signal detection Neyman–Pearson framework Binary hypothesis 

Notes

Acknowledgements

We thank Digital India Corporation under Ministry of Electronics & Information Technology, Government of India (Grant No. U72900MH2001NPL133410) for the financial support. We also express our deep gratitude to the anonymous reviewers for their highly professional recommendations, instructions, and motivation which contributed significantly to improve the quality of this paper.

References

  1. 1.
    Lehmann EL (1986) Testing statistical hypothesis, 2nd edn. Wiley, New YorkCrossRefGoogle Scholar
  2. 2.
    Poor HV (1988) An introduction to signal detection and estimation. Springer-Verlag, New YorkCrossRefGoogle Scholar
  3. 3.
    Kassam SA (1988) Signal detection in non-Gaussian noise. Springer-Verlag, New YorkCrossRefGoogle Scholar
  4. 4.
    Watterson JW (1990) An optimum multilayer perceptron neural receiver for signal detection. IEEE Trans Neural Netw 1(4):298–300CrossRefGoogle Scholar
  5. 5.
    Lippmann RP, Beckman P (1989) Adaptive neural net preprocessing for signal detection in non-Gaussian noise. In: Advances in neural information processing systems, vol 1Google Scholar
  6. 6.
    Michalopoulou Z, Nolta L, Alexandrou D (1995) Performance evaluation of multilayer perceptrons in signal detection and classification. IEEE Trans Neural Netw 6(2):381CrossRefGoogle Scholar
  7. 7.
    Gandhi PP, Ramamurti V (1997) Neural networks for signal detection in non-Gaussian noise. IEEE Trans Signal Process 45(11):2846CrossRefGoogle Scholar
  8. 8.
    Halay N, Todros K, Hero AO (2017) Binary hypothesis testing via measure transformed quasi-likelihood ratio test. IEEE Trans. Signal Process 65:6381–6396MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bell M, Kochman Y (2017) on composite binary hypothesis testing with training data. In: Fifty-fifth annual Allerton conference, pp 1026–1033Google Scholar
  10. 10.
    Naderpour M, Ghobadzadeh A, Tadaion A, Gazor S (2015) Generalized wald test for binary composite hypothesis test. IEEE Signal Process Lett 22:2239–2243CrossRefGoogle Scholar
  11. 11.
    Ma J, Xie J, Gan L (2018) Compressive detection of unknown-parameters signals without signal reconstruction. Signal Process 142:114–118CrossRefGoogle Scholar
  12. 12.
    Audhkhasi K, Osoba O, Kosko B (2016) Noise-enhanced convolutional neural networks. Neural Netw (Elsevier) 78:15–23CrossRefGoogle Scholar
  13. 13.
    Chen H, Varshney PK, Kay SM (2007) Theory of stochastic resonance effects in signal detection: part I fixed detectors. IEEE Trans Signal Process 55(7):3172–3184MathSciNetCrossRefGoogle Scholar
  14. 14.
    Franzke B, Kosko B (2011) Using noise to speed up Morkov chain Monte Carlo estimation. Procedia Comput Sci 53:113–120CrossRefGoogle Scholar
  15. 15.
    Audhkhasi K, Osoba O, Kosko B (2013) Noise benefits in backpropagation and deep bidirectional pre-training. IJCNN, pp 1–8Google Scholar
  16. 16.
    Kay SM (2008) Fundamentals of Statistical signal processing, detection theory, vol 2. Prentice Hall PTR, Upper Saddle RiverGoogle Scholar
  17. 17.
    Guo G, Mandal M, Jing Y (2012) A robust detector of known signal in non-Gaussian noise using threshold system. J Signal Process 92:2676–2688CrossRefGoogle Scholar
  18. 18.
    Urkowitz H (1967) Energy detection of unknown deterministic signals. In: Proceedings of the IEEE, pp 523–531CrossRefGoogle Scholar
  19. 19.
    Han J, Liu H, Sun Q, Huang N (2015) Reconstruction of pulse noisy images via stochastic resonance. Nat Sci Rep. Article number: 10616Google Scholar
  20. 20.
    Wiesenfield K, Moss F (1995) Stochastic resonance and the benefits of noise: from ice ages to crayfish and squids. Nature 373:33–36CrossRefGoogle Scholar
  21. 21.
    Sun Q, Liu H, Huang N, Wang Z, Han J, Li S (2015) Non-linear restoration of pulse and high noisy images via stochastic resonance. Nat Sci Rep. Article number: 16183Google Scholar
  22. 22.
    Jha RK, Biswas PK, Chatterji BN (2012) Contrast enhancement of dark images using stochastic resonance. Image Process IET 6:230–237MathSciNetCrossRefGoogle Scholar
  23. 23.
    Weissman I (2017) Sum of squares of uniform random variables. Stat Prob Lett 129:147–154MathSciNetCrossRefGoogle Scholar
  24. 24.
    Shuhei I, Fabio D, Koh H (2018) Noise-modulated neural networks as an application of stochastic resonance. Neurocomputing 277:29–37CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology PatnaBihta, PatnaIndia

Personalised recommendations