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.
©1993 IEEE. Reprinted, with permission, from IEEE Transactions on Signal Processing, pp.3445-62, Dec. 1993.
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References
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.
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.
T. C. Bell, J. G. Cleary, and I. H. Witten, Text Compression, Prentice-Hall: Englewood Cliffs, NJ 1990.
P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code”, IEEE Trans. Commun., vol. 31, pp. 532–540, 1983.
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.
I. Daubechies, “Orthonormal bases of compactly supported wavelets”, Comm. Pure Appl. Math., vol.41, pp. 909–996, 1988.
I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis”, IEEE Trans. Inform. Theory, vol. 36, pp. 961–1005, Sept. 1990.
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.
W. Equitz and T. Cover, “Successive refinement of information”, IEEE Trans. Inform. Theory, vol. 37, pp. 269–275, March 1991.
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.
N.S. Jayant and P. Noll, Digital Coding of Waveforms, Prentice-Hall: Engle-wood Cliffs, NJ 1984.
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.
J. Kovačeveć and M. Vetterli, “Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn” IEEE Trans. Inform. Theory, vol. 38, pp. 533–555, March, 1992.
T. Lane, Independent JPEG Group’s free JPEG software, available by anonymous FTP at uunet.uu.net in the directory/graphics/jpeg. 1991.
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.
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.
S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation”, IEEE Trans. Pattern Anal. Machine Intell. vol. 11 pp. 674–693, July 1989.
S. Mallat, “Multifrequency channel decompositions of images and wavelet models”, IEEE Trans. Acoust. Speech and Signal Processing, vol. 37, pp. 2091–2110, Dec. 1990.
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.
O. Rioul and M. Vetterli, “Wavelets and signal processing”, IEEE Signal Pro-cessing Magazine, vol. 8, pp. 14–38, Oct. 1991.
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.
J. M. Shapiro, “An Embedded Wavelet Hierarchical Image Coder”, Proc. IEEE Int. Conf. Acoust., Speech, Signal Proc., San Francisco, CA, March 1992.
J. M. Shapiro, “Adaptive multidimensional perfect reconstruction filter banks using McClellan transformations”, Proc. IEEE Int. Symp. Circuits Syst., San Diego, CA, May 1992.
J. M. Shapiro, “An embedded hierarchical image coder using zerotrees of wavelet coefficients”, Proc. Data Compression Conf., Snowbird, Utah, IEEE Computer Society Press, 1993.
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.
Special Issue of IEEE Trans. Inform. Theory, March 1992.
G. Strang, “Wavelets and dilation equations: A brief introduction”, SIAM Review vol. 4, pp. 614–627, Dec 1989.
J. Vaisey and A. Gersho, “Image Compression with Variable Block Size Segmentation”, IEEE Trans. Signal Processing, vol. 40, pp. 2040–2060, Aug. 1992.
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.
G. K. Wallace, “The JPEG Still Picture Compression Standard”, Commun. of the ACM, vol. 34, pp. 30–44, April 1991.
I. H. Witten, R. Neal, and J. G. Cleary, “Arithmetic coding for data compression”, Comm. ACM, vol. 30, pp. 520–540, June 1987.
J. W. Woods ed. Subband Image Coding, Kluwer Academic Publishers, Boston, MA. 1991.
G.W. Wornell, “A Karhunen-Loéve expansion for 1/f processes via wavelets”, IEEE Trans. Inform. Theory, vol. 36, July 1990, pp. 859–861.
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.
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.
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Shapiro, J.M. (2002). Embedded Image Coding Using Zerotrees of Wavelet Coefficients. In: Topiwala, P.N. (eds) Wavelet Image and Video Compression. The International Series in Engineering and Computer Science, vol 450. Springer, Boston, MA. https://doi.org/10.1007/0-306-47043-8_8
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DOI: https://doi.org/10.1007/0-306-47043-8_8
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