Wavelet analysis arose as a generalization of Fourier analysis; it dates back to Alfred Haar, who introduced such functions in 1910. Recently, there has been renewed interest in his ideas, which have been expanded on and are being used extensively in computerized information processing and transmission.

This book consists of four sections and 14 chapters. “The Scalable Structure of Information” includes chapters 1 through 3. “Wavelet Theory” includes chapters 4 through 7. “Wavelet Approximation and Algorithms” comprises chapters 8 through 12. The last two chapters form the section “Wavelet Applications.”

The first section is a rambling discourse in which the authors try to connect wavelets to every aspect of information processing imaginable, from quantum mechanics to musical notation. Such musings may be pleasing to them, but they are more likely to confuse than to enlighten readers. In the next two sections, the tone of the presentation changes from colloquial to very abstract, with the authors giving a comprehensive mathematical theory of wavelet analysis. These sections consist almost exclusively of formulas and proofs, and omit motivation and examples. On the positive side, both the text and the appendix include a generous number of references to the original literature, which will help readers understand the intent and significance of the research. The final section is a survey of wavelet applications in data processing and transmission. The results are impressive, but the descriptions of the procedures are too sketchy to be useful to readers lacking expert knowledge of the field. Many of the proposed techniques are rendered unusable due to their lack of standardization, as is found in JPEG or modem protocols.

The large body of literature on this subject includes several excellent general textbooks. Unfortunately, the answer to the question of whether this textbook is a valuable addition to the literature, and suitable for classroom use (as the book’s cover claims), is mainly no. While it contains an accurate and comprehensive introduction to the mathematical theory, it fails to give readers a clear idea of what wavelets are and in what way the methods that utilize them are superior to similar, established techniques. While the authors use terms such as “scalable” and “hi-pass and lo-pass filters” constantly throughout the text, they never explain their precise meaning. This will leave even knowledgeable readers frustrated. While Springer has taken its usual care with the book’s appearance and layout, the editors have not used equal vigilance in accepting the text.