Open Access

The Optimal Design of Weighted Order Statistics Filters by Using Support Vector Machines

  • Chih-Chia Yao1 and
  • Pao-Ta Yu1
EURASIP Journal on Advances in Signal Processing20062006:024185

https://doi.org/10.1155/ASP/2006/24185

Received: 10 January 2005

Accepted: 7 November 2005

Published: 26 March 2006

Abstract

Support vector machines (SVMs), a classification algorithm for the machine learning community, have been shown to provide higher performance than traditional learning machines. In this paper, the technique of SVMs is introduced into the design of weighted order statistics (WOS) filters. WOS filters are highly effective, in processing digital signals, because they have a simple window structure. However, due to threshold decomposition and stacking property, the development of WOS filters cannot significantly improve both the design complexity and estimation error. This paper proposes a new designing technique which can improve the learning speed and reduce the complexity of designing WOS filters. This technique uses a dichotomous approach to reduce the Boolean functions from 255 levels to two levels, which are separated by an optimal hyperplane. Furthermore, the optimal hyperplane is gotten by using the technique of SVMs. Our proposed method approximates the optimal weighted order statistics filters more rapidly than the adaptive neural filters.

[123456789101112131415161718192021222324252627282930313233343536]

Authors’ Affiliations

(1)
Department of Computer Science and Information Engineering, College of Engineering, National Chung Cheng University

References

  1. Cristianini N, Shawe-Taylor J: An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, Cambridge, UK; 2000.View ArticleMATHGoogle Scholar
  2. Vapnik VN: The Nature of Statistical Learning Theory. Springer, New York, NY, USA; 1995.View ArticleMATHGoogle Scholar
  3. Lee Y-J, Mangasarian OL: SSVM: a smooth support vector machine for classification. Computational Optimization and Applications 2001, 20(1):5-22. 10.1023/A:1011215321374MathSciNetView ArticleMATHGoogle Scholar
  4. Mangasarian OL: Generalized support vector machines. In Advances in Large Margin Classifiers. Edited by: Smola AJ, Bartlett P, Schölkopf B, Schuurmans C. MIT Press, Cambridge, Mass, USA; 2000:135-146.Google Scholar
  5. Mangasarian OL, Musicant DR: Successive overrelaxation for support vector machines. IEEE Transactions on Neural Networks 1999, 10(5):1032-1037. 10.1109/72.788643View ArticleGoogle Scholar
  6. Chapelle O, Haffner P, Vapnik VN: Support vector machines for histogram-based image classification. IEEE Transactions on Neural Networks 1999, 10(5):1055-1064. 10.1109/72.788646View ArticleGoogle Scholar
  7. Guo G, Li SZ, Chan KL: Support vector machines for face recognition. Image and Vision Computing 2001, 19(9-10):631-638. 10.1016/S0262-8856(01)00046-4View ArticleGoogle Scholar
  8. Drucker H, Wu D, Vapnik VN: Support vector machines for spam categorization. IEEE Transactions on Neural Networks 1999, 10(5):1048-1054. 10.1109/72.788645View ArticleGoogle Scholar
  9. Vapnik VN: Statistical Learning Theory. John Wiley & Sons, New York, NY, USA; 1998.MATHGoogle Scholar
  10. Yang R, Gabbouj M, Yu P-T: Parametric analysis of weighted order statistics filters. IEEE Signal Processing Letters 1994, 1(6):95-98. 10.1109/97.295344View ArticleGoogle Scholar
  11. Yu P-T: Some representation properties of stack filters. IEEE Transactions on Signal Processing 1992, 40(9):2261-2266. 10.1109/78.157225View ArticleMATHGoogle Scholar
  12. Yu P-T, Chen R-C: Fuzzy stack filters-their definitions, fundamental properties, and application in image processing. IEEE Transactions on Image Processing 1996, 5(6):838-854. 10.1109/83.503903View ArticleGoogle Scholar
  13. Yu P-T, Coyle EJ: The classification and associative memory capability of stack filters. IEEE Transactions on Signal Processing 1992, 40(10):2483-2497. 10.1109/78.157291View ArticleMATHGoogle Scholar
  14. Yu P-T, Coyle EJ: Convergence behavior and N-roots of stack filters. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990, 38(9):1529-1544. 10.1109/29.60073MathSciNetView ArticleMATHGoogle Scholar
  15. Yu P-T, Liao W-H: Weighted order statistics filters-their classification, some properties, and conversion algorithm. IEEE Transactions on Signal Processing 1994, 42(10):2678-2691. 10.1109/78.324733View ArticleGoogle Scholar
  16. Chakrabarti C, Lucke LE: VLSI architectures for weighted order statistic (WOS) filters. Signal Processing 2000, 80(8):1419-1433. 10.1016/S0165-1684(00)00046-3View ArticleGoogle Scholar
  17. Perry SW, Guan L: Weight assignment for adaptive image restoration by neural networks. IEEE Transactions on Neural Networks 2000, 11(1):156-170. 10.1109/72.822518View ArticleGoogle Scholar
  18. Wong H-S, Guan L: A neural learning approach for adaptive image restoration using a fuzzy model-based network architecture. IEEE Transactions on Neural Networks 2001, 12(3):516-531. 10.1109/72.925555View ArticleGoogle Scholar
  19. Yin L, Astola J, Neuvo Y: Optimal weighted order statistic filters under the mean absolute error criterion. Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP '91), April 1991, Toronto, Ontario, Canada 4: 2529-2532.Google Scholar
  20. Yin L, Astola J, Neuvo Y: A new class of nonlinear filters-neural filters. IEEE Transactions on Signal Processing 1993, 41(3):1201-1222. 10.1109/78.205724View ArticleMATHGoogle Scholar
  21. Yin L, Astola J, Neuvo Y: Adaptive multistage weighted order statistic filters based on the backpropagation algorithm. IEEE Transactions on Signal Processing 1994, 42(2):419-422. 10.1109/78.275617View ArticleGoogle Scholar
  22. Wendt PD, Coyle EJ, Gallagher NC: Stack filters. IEEE Transactions on Acoustics, Speech, and Signal Processing 1986, 34(4):898-911. 10.1109/TASSP.1986.1164871View ArticleGoogle Scholar
  23. Avedillo MJ, Quintana JM, Rodriguez-Villegas E: Simple parallel weighted order statistic filter implementations. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '02), May 2002 4: 607-610.Google Scholar
  24. Gasteratos A, Andreadis I: A new algorithm for weighted order statistics operations. IEEE Signal Processing Letters 1999, 6(4):84-86. 10.1109/97.752061View ArticleGoogle Scholar
  25. Huttunen H, Koivisto P: Training based optimization of weighted order statistic filters under breakdown criteria. Proceedings of the International Conference on Image Processing (ICIP '99), October 1999, Kobe, Japan 4: 172-176.View ArticleGoogle Scholar
  26. Koivisto P, Huttunen H: Design of weighted order statistic filters by training-based optimization. Proceedings of the 6th International Symposium on Signal Processing and Its Applications (ISSPA '01), August 2001, Kuala Lumpur, Malaysia 1: 40-43.View ArticleGoogle Scholar
  27. Marshall S: New direct design method for weighted order statistic filters. IEE Proceedings - Vision, Image, and Signal Processing 2001, 151(1):1-8.View ArticleGoogle Scholar
  28. Yli-Harja O, Astola J, Neuvo Y: Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation. IEEE Transactions on Signal Processing 1991, 39(2):395-410. 10.1109/78.80823View ArticleMATHGoogle Scholar
  29. Bertsekas DP: Nonlinear Programming. Athena Scientific, Belmont, Mass, USA; 1999.MATHGoogle Scholar
  30. Poikonen J, Paasio A: A ranked order filter implementation for parallel analog processing. IEEE Transactions on Circuits and Systems I: Regular Papers 2004, 51(5):974-987. 10.1109/TCSI.2004.827620View ArticleGoogle Scholar
  31. Savin CE, Ahmad MO, Swamy MNS: norm design of stack filters. IEEE Transactions on Image Processing 1999, 8(12):1730-1743. 10.1109/83.806619View ArticleGoogle Scholar
  32. Schlkopf B, Smola AJ: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, Mass, USA; 2002.Google Scholar
  33. Gill PE, Murray W, Wright MH: Practical Optimization. Academic Press, London, UK; 1981.MATHGoogle Scholar
  34. Lee Y-J, Mangasarian OL: RSVM: Reduced Support Vector Machines. Proceedings of the 1st SIAM International Conference on Data Mining, April 2001, Chicago, Ill, USAGoogle Scholar
  35. Stone M: Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society 1974, B36: 111-147.MathSciNetMATHGoogle Scholar
  36. Yin L, Yang R, Gabbouj M, Neuvo Y: Weighted median filters: a tutorial. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 1996, 43(3):157-192. 10.1109/82.486465View ArticleGoogle Scholar

Copyright

© Yao and Yu 2006