Abstract
Hierarchical lossless data compression is a compression technique that has been shown to effectively compress data in the face of uncertainty concerning a proper probabilistic model for the data. In this technique, one represents a data sequence x using one of three kinds of structures: (1) a tree called a pointer tree, which generates x via a procedure called “subtree copying”; (2) a data flow graph which generates x via a flow of data sequences along its edges; or (3) a contextfree grammar which generates x via parallel substitutions accomplished with the production rules of the grammar. The data sequence is then compressed indirectly via compression of the structure which represents it. This article is a survey of recent advances in the rapidly growing field of hierarchical lossless data compression. In the article, we illustrate how the three distinct structures for representing a data sequence are equivalent, outline a simple method for designing compact structures for re presenting a data sequence, and indicate the level of compression performance that can be obtained by compression of the structure representing a data sequence.
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References
Barnsley, M. and L. Hurd. (1993). Fractal Image Compression. Wellesley, MA: AK Peters, Ltd.
Burt, P. and E. Adelson. (1983). “The Laplacian Pyramid as a Compact Image Code,” IEEE Trans. Commun., Vol. 31, pp. 532–540.
Cameron, R. (1988). “Source Encoding Using Syntactic Information Source Models,” IEEE Trans. Inform. Theory, Vol. 34, pp. 843–850.
Chui, C. (1992). (ed.), Wavelets: A Tutorial in Theory and Applications. New York: Academic Press.
Cover, T. and J. Thomas. (1991). Elements of Information Theory. New York: Wiley.
Fisher, Y. (1995). (ed.), Fractal Image Compression: Theory and Application. New York: Springer-Verlag.
Kawaguchi, E. and T. Endo. (1980). “On a Method of Binary-Picture Representation and its Application to Data Compression,” IEEE Trans. Pattern Anal. Machine Intell., Vol. 2, pp. 27–35.
Kieffer, J. and E.-H. Yang. (2000). “Grammar-Based Codes: A New Class of Universal Lossless Source Codes,” IEEE Trans. Inform. Theory, Vol. 46, pp. 737–754.
Kieffer, J., E.-H. Yang, G. Nelson, and P. Cosman. (2000). “Universal Lossless Compression Via Multilevel Pattern Matching,” IEEE Trans. Inform. Theory, Vol. 46, pp. 1227–1245, 2000.
Knuth, D. (1973). The Art of Computer Programming: Volume 1/Fundamental Algorithms. Reading, MA: Addison-Wesley.
Kourapova, E. and B. Ryabko. (1995). “Application of Formal Grammars for Encoding Information Sources,” Probl. Inform. Transm., Vol. 31, pp. 23–26.
Liaw, H-T. and C-S. Liu. (1992). “On the OBDD-Representation of General Boolean Functions,” IEEE Trans. Computers, Vol. 41, pp. 661–664.
Nevill-Manning, C. and I. Witten. (1997a). “Identifying Hierarchical Structure in Sequences: A Linear-Time Algorithm,” Jour. Artificial Intell. Res., Vol. 7, pp. 67–82.
Nevill-Manning, C. and I. Witten. (1997b). “Compression and Explanation Using Hierarchical Grammars,” Computer Journal, Vol. 40, pp. 103–116.
Said, A. and W. Pearlman. (1996). “A New Fast and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees,” IEEE Trans. Circuits Sys. Video Technol., Vol. 6, pp. 243–250.
Shapiro, J. (1993). “Embedded Image Coding Using Zerotrees of Wavelet Coefficients,” IEEE Trans. Signal Proc., Vol. 41, pp. 3445–3462.
Strang, G. and T. Nguyen. (1996). Wavelets and Filter Banks. Wellesley, MA: Wellesley-Cambridge Press.
Yang, E.-H. and J. Kieffer. (2000). “Efficient Universal Lossless Data Compression Algorithms Based on a Greedy Sequential Grammar Transform-Part One: Without Context Models,” IEEE Trans. Inform. Theory, Vol. 46, pp. 755–777.
Ziv, J. and A. Lempel. (1978). “Compression of individual sequences via variablerate coding,” IEEE Trans. Inform. Theory, Vol. 24, pp. 530–536.
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Kieffer, J.C. (2002). A Tutorial on Hierarchical Lossless Data Compression. In: Dror, M., L’Ecuyer, P., Szidarovszky, F. (eds) Modeling Uncertainty. International Series in Operations Research & Management Science, vol 46. Springer, New York, NY. https://doi.org/10.1007/0-306-48102-2_28
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DOI: https://doi.org/10.1007/0-306-48102-2_28
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