Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

When underwater degraded images meet logical stochastic resonance

  • 295 Accesses

  • 1 Citations


Owing to light attenuation and high background noise, underwater images are significantly degraded, which hiders the development of underwater exploration. However, noise itself can be used to counter noise. In this paper, we apply logical stochastic resonance (LSR) to help detect weak objects from low-quality underwater images. On the basis of analysis of the physical character of underwater images, three models, namely basic dynamical system driven by Gaussian noise, basic dynamical system driven by Ornstein–Uhlenbeck (OU) noise, and dynamical system with extra delay loop, are chosen to study the performance of LSR-based object detection. The main workflow of LSR-based object detection is introduced. To analyze the performance of LSR, we perform explicit experiments and systematically discuss the interplay of additional noise with the system parameters. LSR is proven to be helpful in detecting weak objects from low-quality underwater images. Both OU noise and extra delay loop will help the whole system to maintain stability in a higher noisy background.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. 1.

    Duntley, S.Q.: Light in the sea. JOSA 53(2), 214 (1963)

  2. 2.

    Raimondo, S., Silvia, C.: Underwater image processing: state of the art of restoration and image enhancement methods. EURASIP J. Adv. Signal Process. 2010(1), 1–15 (2010)

  3. 3.

    Jaffe, J.S.: Underwater optical imaging: the past, the present, and the prospects. IEEE J. Ocean. Eng. 40(3), 683 (2015)

  4. 4.

    Chiang, J.Y., Chen, Y.C.: Underwater image enhancement by wavelength compensation and dehazing. IEEE Trans. Image Process. 21(4), 1756 (2012)

  5. 5.

    Benzi, R., Sutera, A., Vulpiani, A.: The mechanism of stochastic resonance. J. Phys. A Math. Gen. 14(11), 453 (1981)

  6. 6.

    Chen, H., Varshney, L.R., Varshney, P.K.: Noise-enhanced information systems. Proc. IEEE 102(10), 1607 (2014)

  7. 7.

    Harmer, G., Davis, B., Abbott, D.: A review of stochastic resonance: circuits and measurement. IEEE Trans. Instrum. Meas. 51(2), 299 (2002)

  8. 8.

    Hnggi, P.: Stochastic resonance in biology how noise can enhance detection of weak signals and help improve biological information processing. Chemphyschem A Eur. J. Chem. Phys. Phys. Chem. 3(3), 285 (2002)

  9. 9.

    Mitaim, S., Kosko, B.: Adaptive stochastic resonance in noisy neurons based on mutual information. IEEE Trans. Neural Netw. 15(6), 1526 (2004)

  10. 10.

    Dylov, D.V., Fleischer, J.W.: Nonlinear self-filtering of noisy images via dynamical stochastic resonance. Nat. Photonics 4(5), 323 (2010)

  11. 11.

    Monifi, F., Zhang, J., Özdemir, Ş.K., Peng, B., Liu, Y., Bo, F., Nori, F., Yang, L.: Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nat. Photonics 10(6), 399 (2016)

  12. 12.

    Jha, R.K., Chouhan, R.: Noise-induced contrast enhancement using stochastic resonance on singular values. Signal Image Video Process. 8(2), 339 (2014)

  13. 13.

    Ryu, C., Kong, S.G., Kim, H.: Enhancement of feature extraction for low-quality fingerprint images using stochastic resonance. Pattern Recognit. Lett. 32(2), 107 (2011)

  14. 14.

    Jha, R.K., Biswas, P.K., Shrivastava, S.: Logo extraction using dynamic stochastic resonance. Signal Image Video Process. 7(1), 119 (2013)

  15. 15.

    Rallabandi, V.P., Roy, P.K.: Magnetic resonance image enhancement using stochastic resonance in Fourier domain. Magn. Reson. Imag. 28(9), 1361 (2010)

  16. 16.

    Yang, J.H., Sanjun, M.A.F., Liu, H.G., Zhu, H.: Noise-induced resonance at the subharmonic frequency in bistable systems. Nonlinear Dyn. 87(3), 1721 (2017)

  17. 17.

    Hu, B., Kurths, J., Zhou, C.: Array-enhanced coherence resonance. Nature 437(7059), 601 (2001)

  18. 18.

    Rajamani, S., Rajasekar, S., Sanjuán, M.A.F.: Ghost-vibrational resonance. Commun. Nonlinear Sci. Numer. Simul. 19(11), 4003 (2014)

  19. 19.

    Murali, K., Rajamohamed, I., Sinha, S., Ditto, W.L., Bulsara, A.R.: Realization of reliable and flexible logic gates using noisy nonlinear circuits. Appl. Phys. Lett. 95(19), 194102 (2009)

  20. 20.

    Murali, K., Sinha, S., Ditto, W.L., Bulsara, A.R.: Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor. Phys. Rev. Lett. 102(10), 194102 (2009)

  21. 21.

    Gupta, A., Sohane, A., Kohar, V., Murali, K., Sinha, S.: Noise-free logical stochastic resonance. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 84(2), 055201 (2011)

  22. 22.

    Yang, B., Zhang, X., Luo, M.: When noise-free logical stochastic resonance occurs in a bistable system. Nonlinear Dyn. 87(3), 1957 (2017)

  23. 23.

    Sharma, A., Kohar, V., Shrimali, M.D., Sinha, S.: Realizing logic gates with time-delayed synthetic genetic networks. Nonlinear Dyn. 76(1), 431 (2013)

  24. 24.

    Wang, N., Song, A.: Enhanced logical stochastic resonance in synthetic genetic networks. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2736 (2016)

  25. 25.

    Zhang, H., Yang, T., Xu, W., Xu, Y.: Effects of non-Gaussian noise on logical stochastic resonance in a triple-well potential system. Nonlinear Dyn. 76(1), 649 (2014)

  26. 26.

    Kohar, V., Murali, K., Sinha, S.: Enhanced logical stochastic resonance under periodic forcing. Commun. Nonlinear Sci. Numer. Simul. 19(8), 2866 (2014)

  27. 27.

    Wang, G., Zheng, B., Sun, F.F.: Estimation-based approach for underwater image restoration. Opt. Lett. 36(13), 2384 (2011)

  28. 28.

    Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70(1), 223 (1998)

Download references

Author information

Correspondence to Nan Wang.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript

Additional information

This work was supported by National Natural Science Foundation of China (No. 61703381), Natural Science Foundation of Shandong Province (No. ZR2017BF006), China Postdoctoral Science Foundation (No. 2016M590658) and Fundamental Research Funds for the Central Universities (No. 201713017).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, N., Zheng, B., Zheng, H. et al. When underwater degraded images meet logical stochastic resonance. Nonlinear Dyn 94, 295–305 (2018). https://doi.org/10.1007/s11071-018-4359-y

Download citation


  • Logical stochastic resonance
  • Weak object detection
  • Underwater image processing