Advertisement

Embedded Image Coding Using Zerotrees of Wavelet Coefficients

  • Jerome M. Shapiro
Chapter
Part of the The International Series in Engineering and Computer Science book series (SECS, volume 450)

Abstract

The Embedded Zerotree Wavelet Algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code. The embedded code represents a sequence of binary decisions that distinguish an image from the “null” image. Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly. Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream. In addition to producing a fully embedded bit stream, EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images. Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source.

The EZW algorithm is based on four key concepts: 1) a discrete wavelet transform or hierarchical subband decomposition, 2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, 3) entropy-coded successive-approximation quantization, and 4) universal lossless data compression which is achieved via adaptive arithmetic coding.

Keywords

Wavelet Coefficient Coarse Scale Uncertainty Interval Distortion Function Probability Density Function 
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]
    E.H. Adelson, E. Simoncelli, and R. Hingorani, “Orthogonal pyramid transforms for image coding”, Proc. SPIE, vol. 845, Cambridge, MA, pp. 50–58, Oct. 1987.Google Scholar
  2. [2]
    R. Ansari, H. Gaggioni, and D.J. LeGall, “HDTV coding using a non-rectangular subband decomposition,” Proc. SPIE Conf. Vis. Commun. Image Processing, Cambridge, MA, pp. 821–824, Nov. 1988.Google Scholar
  3. [3]
    T. C. Bell, J. G. Cleary, and I. H. Witten, Text Compression, Prentice-Hall: Englewood Cliffs, NJ 1990.Google Scholar
  4. [4]
    P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code”, IEEE Trans. Commun., vol. 31, pp. 532–540, 1983.CrossRefGoogle Scholar
  5. [5]
    R. R. Coifman and M. V. Wickerhauser, “Entropy-based algorithms for best basis selection”, IEEE Trans. Inform. Theory, vol. 38, pp. 713–718, March, 1992.CrossRefGoogle Scholar
  6. [6]
    I. Daubechies, “Orthonormal bases of compactly supported wavelets”, Comm. Pure Appl. Math., vol.41, pp. 909–996, 1988.zbMATHMathSciNetGoogle Scholar
  7. [7]
    I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis”, IEEE Trans. Inform. Theory, vol. 36, pp. 961–1005, Sept. 1990.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    R. A. DeVore, B. Jawerth, and B. J. Lucier, “Image compression through wavelet transform coding”, IEEE Trans. Inform. Theory, vol. 38, pp. 719–746, March, 1992.CrossRefMathSciNetGoogle Scholar
  9. [9]
    W. Equitz and T. Cover, “Successive refinement of information”, IEEE Trans. Inform. Theory, vol. 37, pp. 269–275, March 1991.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Y. Huang, H. M. Driezen, and N. P. Galatsanos “Prioritized DCT for Compression and Progressive Transmission of Images”, IEEE Trans. Image Processing, vol. 1, pp. 477–487, Oct. 1992.Google Scholar
  11. [11]
    N.S. Jayant and P. Noll, Digital Coding of Waveforms, Prentice-Hall: Engle-wood Cliffs, NJ 1984.Google Scholar
  12. [12]
    Y. H. Kim and J. W. Modestino, “Adaptive entropy coded subband coding of images”, IEEE Trans. Image Process., vol 1, pp. 31–48, Jan. 1992.Google Scholar
  13. [13]
    J. Kovačeveć and M. Vetterli, “Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for RnIEEE Trans. Inform. Theory, vol. 38, pp. 533–555, March, 1992.MathSciNetGoogle Scholar
  14. [14]
    T. Lane, Independent JPEG Group’s free JPEG software, available by anonymous FTP at uunet.uu.net in the directory/graphics/jpeg. 1991.Google Scholar
  15. [15]
    A. S. Lewis and G. Knowles, “A 64 Kb/s Video Codec using the 2-D wavelet transform”, Proc. Data Compression Conf., Snowbird, Utah, IEEE Computer Society Press, 1991.Google Scholar
  16. [16]
    A. S. Lewis and G. Knowles, “Image Compression Using the 2-D Wavelet Transform”, IEEE Trans. Image Processing vol. 1 pp. 244–250, April 1992.Google Scholar
  17. [17]
    S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation”, IEEE Trans. Pattern Anal. Machine Intell. vol. 11 pp. 674–693, July 1989.CrossRefzbMATHGoogle Scholar
  18. [18]
    S. Mallat, “Multifrequency channel decompositions of images and wavelet models”, IEEE Trans. Acoust. Speech and Signal Processing, vol. 37, pp. 2091–2110, Dec. 1990.Google Scholar
  19. [19]
    A. Pentland and B. Horowitz, “A practical approach to fractal-based image compression”, Proc. Data Compression Conf., Snowbird, Utah, IEEE Com-puter Society Press, 1991.Google Scholar
  20. [20]
    O. Rioul and M. Vetterli, “Wavelets and signal processing”, IEEE Signal Pro-cessing Magazine, vol. 8, pp. 14–38, Oct. 1991.Google Scholar
  21. [21]
    A. Said and W. A. Pearlman, “Image Compression using the Spatial-Orientation Tree”, Proc. IEEE Int. Symp. on Circuits and Systems, Chicago, IL, May 1993, pp. 279–282.Google Scholar
  22. [22]
    J. M. Shapiro, “An Embedded Wavelet Hierarchical Image Coder”, Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., San Francisco, CA, March 1992.Google Scholar
  23. [23]
    J. M. Shapiro, “Adaptive multidimensional perfect reconstruction filter banks using McClellan transformations”, Proc. IEEE Int. Symp. Circuits Syst., San Diego, CA, May 1992.Google Scholar
  24. [24]
    J. M. Shapiro, “An embedded hierarchical image coder using zerotrees of wavelet coefficients”, Proc. Data Compression Conf., Snowbird, Utah, IEEE Computer Society Press, 1993.Google Scholar
  25. [25]
    J. M. Shapiro, “Application of the embedded wavelet hierarchical image coder to very low bit rate image coding”, Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., Minneapolis, MN, April 1993.Google Scholar
  26. [26]
    Special Issue of IEEE Trans. Inform. Theory, March 1992.Google Scholar
  27. [27]
    G. Strang, “Wavelets and dilation equations: A brief introduction”, SIAM Review vol. 4, pp. 614–627, Dec 1989.zbMATHMathSciNetGoogle Scholar
  28. [28]
    J. Vaisey and A. Gersho, “Image Compression with Variable Block Size Segmentation”, IEEE Trans. Signal Processing, vol. 40, pp. 2040–2060, Aug. 1992.CrossRefGoogle Scholar
  29. [29]
    M. Vetterli, J. Kovečević and D. J. LeGall, “Perfect reconstruction filter banks for HDTV representation and coding”, Image Commun., vol. 2, pp. 349–364,Oct 1990.Google Scholar
  30. [30]
    G. K. Wallace, “The JPEG Still Picture Compression Standard”, Commun. of the ACM, vol. 34, pp. 30–44, April 1991.Google Scholar
  31. [31]
    I. H. Witten, R. Neal, and J. G. Cleary, “Arithmetic coding for data compression”, Comm. ACM, vol. 30, pp. 520–540, June 1987.CrossRefGoogle Scholar
  32. [32]
    J. W. Woods ed. Subband Image Coding, Kluwer Academic Publishers, Boston, MA. 1991.Google Scholar
  33. [33]
    G.W. Wornell, “A Karhunen-Loéve expansion for 1/f processes via wavelets”, IEEE Trans. Inform. Theory, vol. 36, July 1990, pp. 859–861.CrossRefGoogle Scholar
  34. [34]
    Z. Xiong, N. Galatsanos, and M. Orchard, “Marginal analysis prioritization for image compression based on a hierarchical wavelet decomposition”,Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., Minneapolis, MN, April 1993.Google Scholar
  35. [35]
    W. Zettler, J. Huffman, and D. C. P. Linden, “Applications of compactly supported wavelets to image compression”, SPIE Image Processing and Algorithms, Santa Clara, CA 1990.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Jerome M. Shapiro

There are no affiliations available

Personalised recommendations