The Discrete Wavelet Transform and Wavelet Synopses

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. 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 and continuous data streams.