chapter  2
38 Pages

A Practical Guide to the Implementation of the Wavelet Transform

WithMichael Unser

This chapter describes the various computational approaches available and provides simple implementation recipes that can be of direct use to the practitioner. It starts by reviewing the basic computational tools. The chapter shows how to compute inner products efficiently using discrete convolutions. It also indicates how to handle boundary conditions. The chapter provides a detailed description of Mallat’s fast wavelet algorithm that can be applied to the decomposition of a sig-nal into orthogonal, semi-orthogonal or bi-orthogonal wavelet bases. It dedicates to the redundant types of wavelet transforms which are usually preferable for signal analyses, feature extraction, or detection tasks, for they provide a description that is truly shift-invariant. The chapter considers a particular type of dyadic wavelet frame representation that has a simple reconstruction algorithm associated with it. It concentrates on the analysis aspect of the wavelet transform and describes computational solutions that are not necessarily restricted to scales that are powers of two.