Encyclopedia of Database Systems

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

Discrete Wavelet Transform and Wavelet Synopses

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

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...

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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