Advertisement

A New Fuzzy-Based Wavelet Shrinkage Image Denoising Technique

  • Stefan Schulte
  • Bruno Huysmans
  • Aleksandra Pižurica
  • Etienne E. Kerre
  • Wilfried Philips
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4179)

Abstract

This paper focuses on fuzzy image denoising techniques. In particular, we investigate the usage of fuzzy set theory in the domain of image enhancement using wavelet thresholding. We propose a simple but efficient new fuzzy wavelet shrinkage method, which can be seen as a fuzzy variant of a recently published probabilistic shrinkage method [1] for reducing adaptive Gaussian noise from digital greyscale images. Experimental results show that the proposed method can efficiently and rapidly remove additive Gaussian noise from digital greyscale images. Numerical and visual observations show that the performance of the proposed method outperforms current fuzzy non-wavelet methods and is comparable with some recent but more complex wavelets methods. We also illustrate the main differences between this version and the probabilistic version and show the main improvements in comparison to it.

Keywords

Fuzzy Rule Additive Gaussian Noise Wavelet Shrinkage Shrinkage Method Gaussian Scale Mixture 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pižurica, A., Philips, W.: Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising. IEEE Transactions on Image Process. 15(3), 654–665 (2006)CrossRefGoogle Scholar
  2. 2.
    Resnikoff, H.L., Wells, R.O.: Wavelet Analysis: The Scalable Structure of Information. Springer, Heidelberg (1998)MATHGoogle Scholar
  3. 3.
    Donoho, D.: Denoising by soft-thresholding. IEEE Transactions on Information Theory 41(5), 613–627 (1995)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Donoho, D., Johnstone, I.: Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association 90, 1200–1224 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chang, S., Yu, B., Vetterli, M.: Adaptive wavelet thresholding for image denoising and compression. IEEE Transactions on Image Processing 9(9), 1532–1546 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hansen, M., Yu, B.: Wavelet thresholding via mdl for natural images. IEEE Transactions on Information Theory 46(8), 1778–1788 (2000)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Simoncelli, E., Adelson, E.: Noise removal via Bayesian wavelet coring. In: Proceedings IEEE International Conference on Image Processing (ICIP 1996), Lausanne, Switserland, pp. 379–382 (1996)Google Scholar
  8. 8.
    Moulin, P., Liu, J.: Analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors. IEEE Transactions on Information Theory 45(4), 909–919 (1999)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Pižurica, A., Philips, W., Lemahieu, I., Acheroy, M.: A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising. IEEE Transactions on Image Processing 11(5), 545–557 (2002)CrossRefGoogle Scholar
  10. 10.
    Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using gaussian scale mixtures in the wavelet domain. IEEE Transactions on Image Processing 12(11), 1338–1351 (2003)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Vidakovic, B.: Nonlinear wavelet shrinkage with bayes rules and bayes factors. Journal of the American Statistical Association 93, 173–179 (1998)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Chipman, H., Kolaczyk, E., McCulloch, R.: Adaptive Bayesian wavelet shrinkage. Journal of the American Statistical Association 92, 1413–1421 (1997)MATHCrossRefGoogle Scholar
  13. 13.
    Sendur, L., Selesnick, I.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Transactions on Signal Processing 50(11), 2744–2756 (2002)CrossRefGoogle Scholar
  14. 14.
    Crouse, M., Nowak, R., Baranuik, R.: Wavelet-based statistical signal processing using hidden Markov models. IEEE Transactions on Signal Processing 46(4), 886–902 (1998)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Romberg, J., Choi, H., Baraniuk, R.: Bayesian tree-structured image modeling using wavelet-domain hidden markov models. IEEE Transactions on Image Processing 10, 1056–1068 (2001)CrossRefGoogle Scholar
  16. 16.
    Malfait, M., Roose, D.: Wavelet-based image denoising using a markov random field a priori model. IEEE Transactions on Image Processing 6(4), 549–565 (1997)CrossRefGoogle Scholar
  17. 17.
    Jansen, M., Bultheel, A.: Empirical Bayes approach to improve wavelet thresholding for image noise reduction. Journal of the American Statistical Association 96(454), 629–639 (2001)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Mihcak, M., Kozintsev, I., Ramchandran, K., Moulin, P.: Low complexity image denoising based on statistical modeling of wavelet coefficients. IEEE Signal Processing Letters 6, 300–303 (1999)CrossRefGoogle Scholar
  19. 19.
    Fan, G., Xia, X.: Image denoising using local contextual hidden markov model in the wavelet domain. IEEE Signal Processing Letters 8(5), 125–128 (2001)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Fan, G., Xia, X.: Improved hidden Markov models in the wavelet domain. IEEE Transactions on Signal Processing 49, 115–120 (2001)CrossRefGoogle Scholar
  21. 21.
    Kerre, E.E.: Fuzzy sets and approximate Reasoning. Xian Jiaotong University Press (1998)Google Scholar
  22. 22.
    Tizhoosh, H.R.: Fuzzy-Bildverarbeitung: Einführung in Theorie und Praxis. Springer, Heidelberg (1997)Google Scholar
  23. 23.
    Zadeh, L.A.: Fuzzy Sets. Information and Control 8(3), 338–353 (1965)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Zadeh, L.A.: Fuzzy logic and its application to approximate reasoning. Information Processing 74, 591–594 (1973)Google Scholar
  25. 25.
    Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425–455 (1994)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Van De Ville, D., Nachtegael, M., Van der Weken, D., Kerre, E.E., Philips, W.: Noise reduction by fuzzy image filtering. IEEE Transactions on Fuzzy Systems 11(4), 429–436 (2003)CrossRefGoogle Scholar
  27. 27.
    Schulte, S., De Witte, V., Nachtegael, M., Van der Weken, D., Kerre, E.E.: Fuzzy Random Impulse Noise Reduction Method. Fuzzy Sets and Systems (submitted) (2006)Google Scholar
  28. 28.
    Wang, J.H., Chiu, H.C.: An adaptive fuzzy filter for restoring highly corrupted images by histogram estimation. Proceedings of the National Science Council -Part A 23, 630–643 (1999)Google Scholar
  29. 29.
    Farbiz, F., Menhaj, M.B., Motamedi, S.A.: Edge Preserving Image Filtering based on Fuzzy Logic. In: Proceedings of the 6th EUFIT conference, pp. 1417–1421 (1998)Google Scholar
  30. 30.
    Kwan, H.K., Cai, Y.: Fuzzy filters for image filtering. In: Proceedings of Circuits and Systems (MWSCAS 2002). The 2002 45th Midwest Symposium, pp. III-672–III-675 (2002)Google Scholar
  31. 31.
    Xu, H., Zhu, G., Peng, H., Wang, D.: Adaptive fuzzy switching filter for images corrupted by impulse noise. Pattern Recognition Letters 25, 1657–1663 (2004)CrossRefGoogle Scholar
  32. 32.
    Tolt, G., Kalaykov, I.: Fuzzy-similarity-based Noise Cancellation for Real-time Image Processing. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), vol. 1, pp. 15–18Google Scholar
  33. 33.
    Tolt, G., Kalaykov, I.: Fuzzy-Similarity-Based Image Noise Cancellation. In: Pal, N.R., Sugeno, M. (eds.) AFSS 2002. LNCS, vol. 2275, pp. 408–413. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  34. 34.
    Kuo, Y.H., Lee, C.S., Chen, C.L.: High-stability AWFM filter for signal restoration and its hardware design. Fuzzy Sets and Systems 114(2), 185–202 (2000)MATHCrossRefGoogle Scholar
  35. 35.
    Şendur, L., Selesnick, I.W.: Bivariate Shrinkage Functions for Wavelet-based Image Denoising. IEEE Transactions on Signal Processing 50(11), 2744–2756 (2002)CrossRefGoogle Scholar
  36. 36.
    Balster, E.J., Zheng, Y.F., Ewing, R.L.: Feature-based wavelet shrinkage algorithm for image denoising. IEEE Transactions on Image Process 14(3), 2024–2039 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Stefan Schulte
    • 1
  • Bruno Huysmans
    • 2
  • Aleksandra Pižurica
    • 2
  • Etienne E. Kerre
    • 1
  • Wilfried Philips
    • 2
  1. 1.Department of Applied Mathematics and Computer ScienceGhent UniversityGentBelgium
  2. 2.Dept. of Telecommunications and Information Processing (TELIN), IPIGhent UniversityGentBelgium

Personalised recommendations