An Introduction to Wavelet Analysis

Abstract

In Section 4.7 we introduced orthonormal bases in general Hilbert spaces. The purpose of the current chapter is to present a general way of constructing orthonormal bases with a particular structure in the Hilbert space L ²($\mathbb R$). In contrast to the other topics treated in the book, wavelet analysis is a quite new topic: although the first constructions appeared about 100 years ago, the systematic analysis began around 1982. In 1987, the key concept of a multiresolution analysis was introduced, and shortly hereafter Daubechies used it to construct a special class of orthonormal bases with attractive properties, e.g., in the context of data compression.