Definition
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 via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
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.
Chakrabarti K, Garofalakis MN, Rastogi R, Shim K. Approximate query processing using wavelets. VLDB J. 2001;10(2–3):199–223.
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.
Deligiannakis A, Garofalakis M, Roussopoulos N. Extended wavelets for multiple measures. ACM Trans Database Syst. June 2007;32(2)
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.
Garofalakis M, Gibbons PB. Approximate query processing: taming the terabytes. In: Proceedings of the 27th International Conference on Very Large Data Bases; 2001.
Garofalakis M, Gibbons PB. Probabilistic wavelet synopses. ACM Trans Database Syst. March 2004;29(1)
Garofalakis M, Kumar A. Wavelet synopses for general error metrics. ACM Trans Database Syst. December 2005;30(4)
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.
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.
Jawerth B, Sweldens W. An overview of wavelet based multiresolution analyses. SIAM Rev. 1994;36(3):377–412.
Stollnitz EJ, DeRose TD, Salesin DH. Wavelets for computer graphics – theory and applications. San Francisco: Morgan Kaufmann; 1996.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media, LLC, part of Springer Nature
About this entry
Cite this entry
Garofalakis, M. (2018). Discrete Wavelet Transform and Wavelet Synopses. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_539
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8265-9_539
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8266-6
Online ISBN: 978-1-4614-8265-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering