There is a very large literature on the theoretical underpinnings of the wavelet transform. However, theory must be complemented with a significant amount of practical work. Selection of method, implementation, validation of results, comparison with alternatives – these are all centrally important for the applied scientist or engineer. Turning theory into practice is the theme of this book. Various applications have benefited from the wavelet and other multiscale transforms. In this book, we describe many such applications, and in this way illustrate the theory and practice of such transforms. We describe an ‘embedded systems’ approach to wavelets and multiscale transforms in this book, in that we introduce and appraise appropriate multiscale methods for use in a wide range of application areas.

Astronomy provides an illustrative background for many of the examples used in this book. Chapters 5 and 6 cover problems in remote sensing. Chapter 3, dealing with noise in images, includes discussion on problems of wide relevance. At the time of writing, the authors are applying these methods to other fields: medical image analysis (radiology, for mammography; echocardiology), plasma physics response signals, and others.

Chapter 1 provides an extensive review of the theory and practice of the wavelet transform. This chapter then considers other multiscale transforms, offering possible advantages in regard to robustness. The reader wishing early ‘action’ may wish to read parts of Chapter 1 at first, and dip into it again later, for discussion of particular methods.