Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Discrete Wavelet Transform and Wavelet Synopses

  • Minos GarofalakisEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_539


Wavelets are a useful mathematical tool for hierarchically decomposing functions in ways that are both efficient and theoretically sound. Broadly speaking, the wavelet transform of a function consists of a coarse overall approximation together with detail coefficients that influence the function at various scales. The wavelet transform has a long history of successful applications in signal and image processing [11, 12]. Several recent studies have also demonstrated the effectiveness of the wavelet transform (and Haar wavelets, in particular) as a tool for approximate query processing over massive relational tables [2, 7, 8] and continuous data streams [3, 9]. Briefly, the idea is to apply wavelet transform to the input relation to obtain a compact data synopsis that comprises a select small collection of wavelet coefficients. The excellent energy compaction and de-correlation properties of the wavelet transform allow for concise and effective approximate representations...

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Alon N, Matias Y, Szegedy M. The space complexity of approximating the frequency moments. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing; 1996. p. 20–9.zbMATHGoogle Scholar
  2. 2.
    Chakrabarti K, Garofalakis MN, Rastogi R, Shim K. Approximate query processing using wavelets. VLDB J. 2001;10(2–3):199–223.zbMATHGoogle Scholar
  3. 3.
    Cormode G, Garofalakis M, Sacharidis D. Fast approximate wavelet tracking on streams. In: Advances in Database Technology, Proceedings of the 10th International Conference on Extending Database Technology; 2006.Google Scholar
  4. 4.
    Deligiannakis A, Garofalakis M, Roussopoulos N. Extended wavelets for multiple measures. ACM Trans Database Syst. June 2007;32(2)CrossRefGoogle Scholar
  5. 5.
    Deshpande A, Garofalakis M, Rastogi R. Independence is good: dependency-based histogram synopses for high-dimensional data. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 2001.Google Scholar
  6. 6.
    Garofalakis M, Gibbons PB. Approximate query processing: taming the terabytes. In: Proceedings of the 27th International Conference on Very Large Data Bases; 2001.Google Scholar
  7. 7.
    Garofalakis M, Gibbons PB. Probabilistic wavelet synopses. ACM Trans Database Syst. March 2004;29(1)CrossRefGoogle Scholar
  8. 8.
    Garofalakis M, Kumar A. Wavelet synopses for general error metrics. ACM Trans Database Syst. December 2005;30(4)CrossRefGoogle Scholar
  9. 9.
    Gilbert AC, Kotidis Y, Muthukrishnan S, Strauss MJ. One-pass wavelet decomposition of data streams. IEEE Trans Knowl Data Eng. May 2003;15(3):541–54.CrossRefGoogle Scholar
  10. 10.
    Guha S, Harb B. Wavelet synopsis for data streams: minimizing non-euclidean error. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; 2005.p. 88–97.Google Scholar
  11. 11.
    Jawerth B, Sweldens W. An overview of wavelet based multiresolution analyses. SIAM Rev. 1994;36(3):377–412.CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Stollnitz EJ, DeRose TD, Salesin DH. Wavelets for computer graphics – theory and applications. San Francisco: Morgan Kaufmann; 1996.Google Scholar
  13. 13.
    Vitter JS, Wang M. Approximate computation of multidimensional aggregates of sparse data using wavelets. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1999. p. 193–204.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Technical University of CreteChaniaGreece

Section editors and affiliations

  • Xiaofang Zhou
    • 1
  1. 1.School of Inf. Tech. & Elec. Eng.Univ. of QueenslandBrisbaneAustralia