Wavelets

Wavelet techniques have been in efficient practical use for less than two decades. They complement classical Fourier methods. The two most successful applications of wavelet techniques are found in image processing and in noise reduction.

The present book gives an overview and an introduc [...]
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Wavelet techniques have been in efficient practical use for less than two decades. They complement classical Fourier methods. The two most successful applications of wavelet techniques are found in image processing and in noise reduction.

The present book gives an overview and an introduction to the theory and its applications. It is written for a reader who has some familiarity   with Fourier methods and linear algebra. Essentially, it explains what wavelets are, and how the techniques are applied, with a minimum of  mathematical details.

The book is divided into two parts: the first devoted to theory and the second to applications. The chapters on filter banks and multiresolution analysis are basic. Subsequent chapters are built on these, and can be read independently of each other. There is also an introduction, in which we roughly sketch some key ideas and applications.

In the theoretical part, we first review the foundations of signal processing, and go on with filter banks. The main chapter of this part treats multiresolution analysis and wavelets. We end the first part with chapters on wavelets in more than one dimension, lifting, and the con-tinuous wavelet transform.

In the applications part, we first present some of the most well-known wavelet bases. Next, we discuss adaptive bases, compression and noise reduction, followed by wavelet methods for the numerical treatment of, among other things, partial differential equations. Finally, we describe differentiability in wavelet representations, an application of the continuous wavelet transform, feature extraction, and some implementation issues.