ABSTRACT
This chapter introduces basic knowledge of the wavelet theory that is related to this book. Starting from classical wavelets on Euclidean domains, it turns to wavelet design on structure data: graphs, meshes, and manifolds.
As by its name, a wavelet is a function that oscillates like a wave along its domain, with attenuated amplitude that makes it locally-supported by a bounded region. It is much easier to get a first impression on wavelet by looking at some well-known examples in Fig. 2.1. Rather than theorems and equations, we would like to use three basic features for the first impression of wavelet: oscillation, attenuation, and multiscale.
