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Evolving Wavelets Using a Coevolutionary Genetic Algorithm and Lifting

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Genetic and Evolutionary Computation – GECCO 2004 (GECCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3103))

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Abstract

Finding a good wavelet for a particular application and type of input data is a difficult problem. Traditional methods of wavelet design focus on abstract properties of the wavelet that can be optimized analytically but whose influence on its real-world performance are not entirely understood. In this paper, a coevolutionary genetic algorithm is developed that searches the space of biorthogonal wavelets. The lifting technique, which defines a wavelet as a sequence of digital filters, provides a compact representation and an efficient way of handling necessary constraints. The algorithm is applied to a signal compression task with good results.

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References

  1. Gomez, F., Miikkulainen, R.: Solving non-markovian control tasks with neuroevolution. In: Proceedings of the International Joint Conference on Artificial Intelligence, San Francisco, CA, pp. 1356–1361 (1999)

    Google Scholar 

  2. Jawerth, B., Sweldens, W.: An overview of wavelet based multiresolution analyses. SIAM Rev. 36, 377–412 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Daubechies, I., Sweldens, W.: Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications 4, 245–267 (1998)

    Article  MathSciNet  Google Scholar 

  4. Davis, G., Nosratinia, A.: Wavelet-based image coding: An overview. Applied and Computational Control, Signals and Circuits 1 (1998)

    Google Scholar 

  5. Sweldens, W.: The lifting scheme: A custom-design construction of biorthogonal wavelets. Journal of Applied and Computational Harmonic Analysis 3, 186–200 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Coifman, R., Wickerhauser, V.: Entropy-based algorithms for best basis selection. IEEE Transactions on Information Theory 38, 713–718 (1992)

    Article  MATH  Google Scholar 

  7. Wickerhauser, M.: Adapted Wavelet Analysis from Theory to Software. A. K. Peters, Wellesley (1994)

    MATH  Google Scholar 

  8. Lankhorst, M.M., van der Laan, M.D.: Wavelet-based signal approximation with genetic algorithms. Evolutionary Programming, 237–255 (1995)

    Google Scholar 

  9. Liu, C., Wechsler, H.: Face recognition using evolutionary pursuit. In: Proceedings of the Fifth European Conference on Computer Vision, Freiburg, Germany (1998)

    Google Scholar 

  10. Claypoole, R., Braniuk, R., Nowak, R.: Adaptive wavelet transforms via lifting. In: Transactions of the International Conference on Acoustics, Speech and Signal Processing, pp. 1513–1516 (1998)

    Google Scholar 

  11. Erba, M., Rossi, R.: Liberali, V., Tettamanzi, A.: Digital filter design through simulated evolution. In: Proceedings of the ECCTD 2001, Espoo, Finland (2001)

    Google Scholar 

  12. Lee, A., Ahmadi, M., Jullien, G., Miller, W., Lashkari, R.: Design of 1-d fir filters with genetic algorithms. In: ISSPA 5th International Symposium, pp. 955–958 (1999)

    Google Scholar 

  13. Monro, D., Sherlock, B.: Space-frequency balance in biorthogonal wavelets. Transactions of the IEEE Int. Conf. on Image Processing 1, 624–627 (1997)

    Google Scholar 

  14. Hill, Y., O’Keefe, S., Thiel, D.: An investigation of wavelet design using genetic algorithms. In: Microelectronic Engeneering Research Conference (2001)

    Google Scholar 

  15. Villasenor, J., Belzer, B., Lia, J.: Wavelet filter evaluation for image compression. IEEE Transactions on Image Processing 2, 1053–1060 (1995)

    Article  Google Scholar 

  16. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math., 909–996 (1988)

    Google Scholar 

  17. Antonini, M., Barlaud, M., Mathieu, P., Daubechies, I.: Image coding using wavelet transform. IEEE Transactions on Image Processing (1992)

    Google Scholar 

  18. Sweldens, W.: The lifting scheme: A construction of second-generation wavelets. SIAM J. Math. Anal. 29, 511–546 (1997)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Sciences, University of Texas at Austin, Austin, TX, 78712, USA

    Uli Grasemann & Risto Miikkulainen

Authors
  1. Uli Grasemann
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  2. Risto Miikkulainen
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Editor information

Editors and Affiliations

  1. Indian Institute of Technology Kanpur, Department of Mechanical Engineering, Kanpur Genetic Algorithms Laboratory (KanGAL), Kanpur, 208016, Uttar Pradesh, India

    Kalyanmoy Deb

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© 2004 Springer-Verlag Berlin Heidelberg

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Grasemann, U., Miikkulainen, R. (2004). Evolving Wavelets Using a Coevolutionary Genetic Algorithm and Lifting. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_109

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  • DOI: https://doi.org/10.1007/978-3-540-24855-2_109

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22343-6

  • Online ISBN: 978-3-540-24855-2

  • eBook Packages: Springer Book Archive

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