Skip to main content
SpringerLink
Log in

An adaptive fuzzy filter for image denoising

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

This study considers the problem of fuzzy modeling of the images in pixel domain. A zero-order Takagi–Sugeno type fuzzy model provides fuzzy smoothing to the image intensities for removing the additive noise from an image. An adaptive fuzzy filtering algorithm is suggested for estimating the parameters of the fuzzy model with noisy image data. The mathematical analysis of the proposed filtering algorithm has been provided in both deterministic and stochastic framework. The deterministic robustness of the filtering algorithm was shown by deriving an upper bound on the magnitude of estimation errors. The fuzzy filtering algorithm doesn’t demand Gaussian assumption of the noise and is also optimal in the “sense” of variation Bayes towards Student-t distributed noises.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Choi, Y., Krishnapuram, R.: A robust approach to image enhancement based on fuzzy logic. IEEE Trans. Image Process. 6(6), 808–825 (1997)

    Article  Google Scholar 

  2. Lee, C.S., Kuo, Y.H., Yu, P.T.: Weighted fuzzy mean filters for image processing. Fuzzy Sets Syst. 89(2), 157–180 (1997)

    Article  Google Scholar 

  3. Russo, F., Ramponi, G.: A fuzzy operator for the enhancement of blurred and noisy images. IEEE Trans. Image Process. 4(8), 1169–1174 (1995)

    Article  Google Scholar 

  4. Russo, F., Ramponi, G.: A fuzzy filter for images corrupted by impulse noise. IEEE Signal Process. Lett. 3(6), 168–170 (1996)

    Article  Google Scholar 

  5. Schulte, S., Witte, V.D., Kerre, E.E.: A fuzzy noise reduction method for color images. IEEE Trans. Image Process. 16(5), 1425–1436 (2007)

    Article  MathSciNet  Google Scholar 

  6. Ville, D.V.D., Nachtegael, M., Weken, D.V., Kerre, E.E., Philips, W., Lemahieu, I.: Noise reduction by fuzzy image filtering. IEEE Trans. Fuzzy Syst. 11(4), 429–436 (2003)

    Article  Google Scholar 

  7. Wong, A., Mishra, A., Bizheva, K., Clausi, D.A.: General bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery. Optics Express 18(8), 8338–8352 (2010)

    Article  Google Scholar 

  8. Pižurica, A., Philips, W., Lemahieu, I., Acheroy, M.: A joint inter- and intrascale statistical model for bayesian wavelet based image denoising. IEEE Trans. Image Process. 11(5), 545–557 (2002)

    Article  Google Scholar 

  9. Portilla, J., Strela, V., Wainwright, M.J., Simoncelli, E.P.: Image denosing using scale mixtures of gaussians in the Wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003)

    Article  MathSciNet  Google Scholar 

  10. Şendur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Signal Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  11. Barash, D., Comaniciu, D.: A common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift. Image Vis. Comput. 22(1), 73–81 (2004)

    Article  Google Scholar 

  12. Awate, S.P., Whitaker, R.T.: Unsupervised, information-theoretic, adaptive image filtering for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 28(3), 364–376 (2006)

    Article  Google Scholar 

  13. Bezdek, J.C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981)

    Book  Google Scholar 

  14. Burger, M., Haslinger, J., Bodenhofer, U.: Regularized data-driven construction of fuzzy controllers. J. Inverse Ill-Posed Probl. 10, 319–344 (2002)

    Article  MathSciNet  Google Scholar 

  15. Chuang, C.C., Su, S.F., Chen, S.S.: Robust TSK fuzzy modeling for function approximation with outliers. IEEE Trans. Fuzzy Syst. 9(6), 810–821 (2001)

    Article  Google Scholar 

  16. Hong, X., Harris, C.J., Chen, S.: Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality. IEEE Trans. Syst. Man. Cybern. B 34(1), 598–608 (2004)

    Article  Google Scholar 

  17. Johansen, T.: Robust identification of Takagi-Sugeno-Kang fuzzy models using regularization. In: Proceedings of IEEE Conference on Fuzzy Systems, pp. 180–186. New Orleans, USA (1996)

  18. Juang, C.F., Hsieh, C.D.: TS-fuzzy system-based support vector regression. Fuzzy Sets Syst. 160(17), 2486–2504 (2009)

    Article  MathSciNet  Google Scholar 

  19. Juang, C.F., Huang, R.B., Cheng, W.Y.: An interval type-2 fuzzy-neural network with support-vector regression for noisy regression problems. IEEE Trans. Fuzzy Syst. 18(4), 686–699 (2010)

    Article  Google Scholar 

  20. Kim, J., Suga, Y., Won, S.: A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism. IEEE Trans. Fuzzy Syst. 14(2), 222–231 (2006)

    Article  Google Scholar 

  21. Kumar, M., Stoll, N., Stoll, R.: An energy-gain bounding approach to robust fuzzy identification. Automatica 42(5), 711–721 (2006)

    Article  MathSciNet  Google Scholar 

  22. Kumar, M., Stoll, R., Stoll, N.: SDP and SOCP for outer and robust fuzzy approximation. In: Proceedings of 7th IASTED International Conference on Artificial Intelligence and Soft Computing. Banff, Canada (2003)

  23. Kumar, M., Stoll, R., Stoll, N.: Robust adaptive identification of fuzzy systems with uncertain data. Fuzzy Optim. Decis. Mak. 3(3), 195–216 (2004)

    Article  Google Scholar 

  24. Kumar, M., Stoll, R., Stoll, N.: Robust solution to fuzzy identification problem with uncertain data by regularization. Fuzzy approximation to physical fitness with real world medical data: An application. Fuzzy Optim. Decis. Mak. 3(1), 63–82 (2004)

    Article  MathSciNet  Google Scholar 

  25. Kumar, M., Stoll, R., Stoll, N.: Deterministic approach to robust adaptive learning of fuzzy models. IEEE Trans. Syst. Man. Cybern. B 36(4), 767–780 (2006)

    Article  Google Scholar 

  26. Kumar, M., Stoll, R., Stoll, N.: A min-max approach to fuzzy clustering, estimation, and identification. IEEE Trans. Fuzzy Syst. 14(2), 248–262 (2006)

    Article  Google Scholar 

  27. Kumar, M., Stoll, R., Stoll, N.: A robust design criterion for interpretable fuzzy models with uncertain data. IEEE Trans. Fuzzy Syst. 14(2), 314–328 (2006)

    Article  Google Scholar 

  28. Kumar, M., Weippert, M., Arndt, D., Kreuzfeld, S., Thurow, K., Stoll, N., Stoll, R.: Fuzzy filtering for physiological signal analysis. IEEE Trans. Fuzzy Syst. 18(1), 208–216 (2010). https://doi.org/10.1109/TFUZZ.2009.2038709

    Article  Google Scholar 

  29. Leski, J.M.: TSK-fuzzy modeling based on \(\epsilon \)-insensitive learning. IEEE Trans. Fuzzy Syst. 13(2), 181–193 (2005)

    Article  MathSciNet  Google Scholar 

  30. Wang, L., Mu, Z., Guo, H.: Fuzzy rule-based support vector regression system. J. Control Theory Appl. 3(3), 230–234 (2005)

    Article  MathSciNet  Google Scholar 

  31. Wang, W.Y., Lee, T.T., Liu, C.L., Wang, C.H.: Function approximation using fuzzy neural networks with robust learning algorithm. IEEE Trans. Syst. Man. Cybern. B 27, 740–747 (1997)

    Article  Google Scholar 

  32. Yu, W., Li, X.: Fuzzy identification using fuzzy neural networks with stable learning algorithms. IEEE Trans. Fuzzy Syst. 12(3), 411–420 (2004)

    Article  Google Scholar 

  33. Kumar, M., Stoll, N., Stoll, R.: Adaptive fuzzy filtering in a deterministic setting. IEEE Trans. Fuzzy Syst. 17(4), 763–776 (2009)

    Article  Google Scholar 

  34. Kumar, M., Stoll, N., Stoll, R.: On the estimation of parameters of takagi-sugeno fuzzy filters. IEEE Trans. Fuzzy Syst. 17(1), 150–166 (2009)

    Article  Google Scholar 

  35. Kumar, M., Stoll, N., Stoll, R., Thurow, K.: A stochastic framework for robust fuzzy filtering and analysis of signals—Part I. IEEE Trans. Cybern. 46(5), 1118–1131 (2016). https://doi.org/10.1109/TCYB.2015.2423657

    Article  Google Scholar 

  36. Kumar, M., Insan, A., Stoll, N., Thurow, K., Stoll, R.: Stochastic fuzzy modeling for ear imaging based child identification. IEEE Trans. Syst. Man Cybern. Syst. 46(9), 1265–1278 (2016). https://doi.org/10.1109/TSMC.2015.2468195

    Article  Google Scholar 

  37. Kumar, M., Mao, Y., Wang, Y., Chenggen, Y., Zhang, W.: Fuzzy theoretic approach to signals and systems: static systems. Inf. Sci. 418, 668–702 (2017). https://doi.org/10.1016/j.ins.2017.08.048

    Article  Google Scholar 

  38. Attias, H.: A variational Bayesian framework for graphical models. In: In Advances in Neural Information Processing Systems 12, pp. 209–215. MIT Press, Cambridge (2000)

  39. Beal, M.J.: Variational algorithms for approximate Bayesian inference. Ph.D. thesis, The Gatsby Computational Neuroscience Unit, University College London, London, UK (2003)

  40. Lappalainen, H., Miskin, J.W.: Ensemble learning. Advances in Independent Component Analysis. Springer, Berlin (2000)

    Google Scholar 

  41. Christmas, J., Everson, R.: Robust autoregression: Student-t innovations using variational Bayes. IEEE Trans. Signal Process. 59(1), 48–57 (2011)

    Article  MathSciNet  Google Scholar 

  42. Tipping, M.E., Lawrence, N.D.: Variational inference for Student-t models: Robust Bayesian interpolation and generalised component analysis. Neurocomputing 69, 123–141 (2005)

    Article  Google Scholar 

Download references

Acknowledgments

Funding was provided by National Natural Science Foundation of China (ID0EQOAE4397).

Author information

Authors and Affiliations

  1. Department of Electronic Information Engineering, Nanchang University, Nanchang, China

    Weiping Zhang

  2. Binhai Industrial Technology Research Institute of Zhejiang University, Tianjin, 300301, China

    Mohit Kumar & Jingzhi Yang

  3. Zhejiang University College of Civil Engineering and Architecture, Hangzhou, 310027, China

    Yunfeng Zhou & Yihua Mao

  4. Faculty of Computer Science and Electrical Engineering, University of Rostock, 18055, Rostock, Germany

    Mohit Kumar

Authors
  1. Weiping Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingzhi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yunfeng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yihua Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yihua Mao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, W., Kumar, M., Yang, J. et al. An adaptive fuzzy filter for image denoising. Cluster Comput 22 (Suppl 6), 14107–14124 (2019). https://doi.org/10.1007/s10586-018-2253-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-018-2253-5

Keywords

Search

Navigation