Advertisement

Efficient compression of wavelet coefficients for smooth and fractal-like data

  • Karel CulikII
  • Simant Dube
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

We show how to integrate wavelet-based and fractal-based approaches for data compression. If the data is self-similar or smooth then one can efficiently store its wavelet coefficients using fractal compression techniques resulting in high compression ratios.

Keywords

Wavelet Coefficient Compression Method Haar Wavelet Iterate Function System Efficient Compression 
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.
    Barnsley, M. F.: Fractals Everywhere. Academic Press (1988)Google Scholar
  2. 2.
    Berstel, J., Reutenauer, Ch.: Rational Series and Their Languages. Springer-Verlag, Berlin (1988)Google Scholar
  3. 3.
    Culik II, K., and Dube S.: Encoding Images as Words and Languages. International Journal of Algebra and Computation (to appear)Google Scholar
  4. 4.
    Culik II, K., and Dube S.: Implementing Wavelet Transform with Automata and Applications to Data Compression. Manuscript (submitted to Graphical Models & Image Processing)Google Scholar
  5. 5.
    Culik II, K., Dube S., Rajcany, P.: Efficient Compression of Wavelet Coefficients for Smooth and Fractal-Eke Data. Manuscript (submitted to CDD'93)Google Scholar
  6. 6.
    Culik II, K., Karhumäki, J.: Finite Automata Computing Real Functions. TR 9105, Univ. of South Carolina (1991) (submitted to SIAM J. on Computing)Google Scholar
  7. 7.
    Culik II, K., Kari, J.: Image Compression Using Weighted Finite Automata. (1992) (submitted to Computer & Graphics)Google Scholar
  8. 8.
    Daubechies, I.: Orthonormal Basis of Compactly Supported Wavelets. Communications on Pure and Applied Math. 41 (1988) 909–996Google Scholar
  9. 9.
    DeVore, R. A., Jawerth, B., Lucier, B.J.: Image Compression through Wavelet Transform Coding. IEEE Transactions on Information Theory 38 (1991) 719–746Google Scholar
  10. 10.
    Eilenberg, S.: Automata, Languages and Machines. Vol. A, Academic Press, New York (1974)Google Scholar
  11. 11.
    Fisher, Y.: Fractal Image Compression. Course Notes, SIGGRAPH'92.Google Scholar
  12. 12.
    Mallat, S. G.: A Theory of Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence. 11 (1989) 674–693Google Scholar
  13. 13.
    Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, Berlin (1978)Google Scholar
  14. 14.
    Strang, G.: Wavelets and Dilation Equations: A Brief Introduction. SIAM Review 31 4 (1989) 614–627Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Karel CulikII
    • 1
  • Simant Dube
    • 2
  1. 1.Dept. of Computer ScienceUniversity of South CarolinaColumbiaUSA
  2. 2.Dept. of Math., Stat. and Comp. Sci.University of New EnglandArmidaleAustralia

Personalised recommendations