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Low Bit-Rate Design Considerations for Wavelet-Based Image Coding

  • Michael Lightstone
  • Eric Majani
  • Sanjit K. Mitra
Chapter

Abstract

Biorthogonal and orthogonal filter pairs derived from the family of binomial product filters are considered for wavelet transform implementation with the goal of high performance lossy image compression. Using experimental rate-distortion performance as the final measure of comparison, a number of new and existing filters are presented with excellent image coding capabilities. In addition, numerous filter attributes such as orthonormality, transition band sharpness, coding gain, low-band reconstruction error, regularity, and vanishing moments are assessed to determine their importance with regards to the fidelity of the decoded images. While image data compression is specifically addressed, many of the proposed techniques are applicable to other coding applications.

Key Words

wavelets image coding filter design 

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References

  1. 1.
    P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englewood Cliffs, NJ: Prentice Hall, 1993.MATHGoogle Scholar
  2. 2.
    M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. on Signal Processing, vol. 40, 1992, pp. 2207–2232.MATHCrossRefGoogle Scholar
  3. 3.
    J. D. Johnston, “A filter family designed for use in quadrature mirror filter banks,” in Proc. of the Int. Conf. on Acoust. Speech and Sig. Proc., 1980, pp. 291–294.Google Scholar
  4. 4.
    F. Grenez, “Chebyshev design of filters for subband coders,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 36, 1988, pp. 182–185.Google Scholar
  5. 5.
    M. J. T. Smith and T. P. Barnwell, “Exact reconstruction techniques for tree-structured subband coders,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 34, 1986, pp. 434–441.Google Scholar
  6. 6.
    J. W. Woods and S. D. O’Neil, “Subband coding of images,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 34, 1986, pp. 1278–1288.Google Scholar
  7. 7.
    I. Daubechies, Ten Lectures on Wavelets, Philadelphia, PA: SIAM, 1992.MATHCrossRefGoogle Scholar
  8. 8.
    A. Gersho and R. M. Gray, Vector Quantization and Signal Compression, Boston: Kluwer Academic Publishers, 1992.MATHCrossRefGoogle Scholar
  9. 9.
    J. Katto and Y. Yasuda, “Performance evaluation of subband coding and optimization of its filter coefficients,” in Proc. of the SPIE Symposium on Visual Comm. and Image Proc., vol. 1605, 1991, pp. 95–106.Google Scholar
  10. 10.
    M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, “Image coding using the wavelet transform,” IEEE Trans. on Image Processing, vol. 1, 1992, pp. 205–220.CrossRefGoogle Scholar
  11. 11.
    I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications on Pure and Applied Mathematics, vol. XLI, 1988, pp. 909–996.Google Scholar
  12. 12.
    D. L. Gall and A. Tabatabai, “Subband coding of digital images using symmetric short kernal filters and arithmetic coding techniques,” in Proc. of the Int. Conf. on Acoust. Speech and Sig. Proc., 1988, pp. 761–764.Google Scholar
  13. 13.
    R. Ansari and D. L. Gall, “Advanced television coding using exact reconstruction filter banks,” in J. W. Woods (ed.), Subband Image Coding, Boston, MA: Kluwer Academic Publishers, 1991, pp. 273–318.Google Scholar
  14. 14.
    E. Majani and M. Lightstone, “Wavelet compression of seismic data,” Int. Conf. on Wavelets, Theory, Algorithms, and Applications, Taorimina, Italy, 1993, pp. 14–20.Google Scholar
  15. 15.
    M. Lightstone and E. Majani, “Low bit-rate design considerations for wavelet-based image coding,” in Proc. of the SPIE Symposium on Visual Comm. and Image Proc., vol. 2308, Chicago, IL, 1994, pp. 501–512.Google Scholar
  16. 16.
    E. Majani and M. Lightstone, Biorthogonal wavelets for data compression, in Proceedings of the Data Compression Conference, Snowbird, UT, 1994, p. 462.Google Scholar
  17. 17.
    J. N. Bradley, C. M. Brislawn, and T. Hopper, “The FBI wavelet/scalar quantization for gray-scale fingerprint image compression,” Los Alamos Technical Report,vol. LA-UR-93–1659.Google Scholar
  18. 18.
    A. V. Oppenheim and R. W. Schafer, Discrete-time signal processing, Englewood Cliffs, NJ: Prentice-Hall, 1989.MATHGoogle Scholar
  19. 19.
    A. K. Soman and P. P. Vaidyanathan, “Coding gain in paraunitary analysis/synthesis systems,” IEEE Trans. on Signal Processing, vol. 41, 1993, pp. 1824–1835.MATHCrossRefGoogle Scholar
  20. 20.
    I. Djokovic and P. P. Vaidyanathan, “Statistical wavelet and filter bank optimization,” in Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, vol. 2, 1993, pp. 911–915.Google Scholar
  21. 21.
    N. S. Jayant and P. Noll, Digital coding of waveforms, Englewood Cliff, New Jersey: Prentice-Hall, 1984.Google Scholar
  22. 22.
    J. D. Villasenor, B. Belzer, and J. Liao, “Filter evaluation and selection in wavelet image compression,” in Proceedings of the Data Compression Conference, Snowbird, UT, 1994, pp. 351–360.Google Scholar
  23. O. Rioul, “Simple regularity criteria for subdivision schemes,” SIAMJ. Math. Anal.,vol. 23, 1992, pp. 1544–1576.Google Scholar
  24. 24.
    E. Majani, Biorthogonal wavelets for image compression, in Proc. of the SPIE Symposium on Visual Comm. and Image Proc., vol. 2308, Part 1, Chicago, IL, 1994, pp. 478–488.Google Scholar
  25. 25.
    R. M. de Queiroz and H. S. Malvar, “On the asymptotic performance of hierarchical transforms,” IEEE Trans. on Signal Processing, vol. 40, 1992, pp. 2620–2622.CrossRefGoogle Scholar
  26. 26.
    J. M. Shapiro, “An embedded wavelet hierarchical image coder,” in Proc. of the Int. Conf. on Acoust. Speech and Sig. Proc., 1992, p. 1992.Google Scholar
  27. 27.
    J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. on Signal Processing, vol. 41, 1993, pp. 3445–3462.MATHCrossRefGoogle Scholar
  28. 28.
    C. Herley and M. Vetterli, “Orthogonal time-varying filter banks and wavelet packets,” IEEE Trans. on Signal Processing, vol. 42, 1994, pp. 2650–2663.CrossRefGoogle Scholar
  29. 29.
    M. J. T. Smith and S. L. Eddins, “Analysis/synthesis techniques for subband image coding,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 38, 1990, pp. 1446–1456.Google Scholar
  30. 30.
    G. Karlsson and M. Vetterli, “Extension of finite length signals for subband image coding, ” Signal Processing, vol. 17, 1989, pp. 161–168.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Michael Lightstone
    • 1
  • Eric Majani
    • 2
  • Sanjit K. Mitra
    • 3
  1. 1.Chromatic Research CorporationSunnyvaleUSA
  2. 2.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA
  3. 3.Center for Information Processing Research, Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

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