Chapter 4: Discrete and Continuous Wavelet Transforms

Continuing from Chapter 3, in this chapter we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects. We outline some new links between the two transform technologies based on the theory of representations of generators and relations. By this we mean a finite system of generators which are represented by operators in Hilbert space. We further outline how these representations yield subband filter banks for signal and image processing algorithms. This chapter is inspired by [JS14a]. This builds more mathematical theory to discrete wavelet transforms discussed in Chapter 3 with wavelet image compression examples…