Wavelets and their Applications

Chapter 9

An Overview of Applications

9.1. Introduction

9.1.1. Why does it work?

As this chapter shows, wavelets are used in a large number of fields. Let us just mention geophysics, astrophysics, quality control, biology and aural signals in medicine, imagery in all its aspects and medical imagery in particular, compressed representation of fingerprints or photographs, satellite imagery, coding of video signals, modeling of traffic in communication networks like the Internet and analysis of atmospheric or wind tunnel turbulence. Even after years of work we remain surprised by the variety of domains concerned and the problems dealt with.

A question arises from the start: how is it possible that the same tool works for so many applications? Of course, it is impossible to find a single really satisfactory answer, but several reasons appear plausible. In his book of historical presentation of wavelets, Hubbard (see [HUB 95] p. 139-173) proposes several clues on very diverse levels:

– first of all, the wavelets method is new in signal processing. It brings technical innovations and makes it possible to look at traditional information through original easily accessible tools. A new dictionary of shapes is created, connecting signal characteristics to those of wavelet transforms, enabling us to infer properties of the signals based on coefficient structures. There are, for example, visible cones in continuous decomposition, which indicate a serious signal irregularity. It is also known ...