We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.
Wavelets form a versatile tool for representing general functions or data sets.
Essentially we can think of them as data building blocks. Galerkin scheme of the time dependent Maxwell s equations. Doc 70 Wavelets on closed subsets of the real line - Andersson, Hall et al. Wavelet transforms that map integers to integers - Calderbank, Daubechies et al. Doc 39 Existence and global regularity of solutions - Daubechies, Lagarias et al.