Fundamentals of wavelets. Theory, algorithms, and applications. 2nd ed.

*(English)*Zbl 1214.65071
Wiley Series in Microwave and Optical Engineering. Hoboken, NJ: John Wiley & Sons (ISBN 978-0-470-48413-5/hbk; 978-0-470-92699-4/ebook). xviii, 359 p. (2011).

This well-written textbook is an essential introduction to the theory, algorithms and applications of wavelets from an engineering point of view. The reader can easily learn the subject and the applications to practical problems. The book consists of 10 chapters. Chapter 1 gives an overview of the book. In Chapters 2 and 3, some basic concepts of linear algebra, Fourier analysis, and digital signal processing are reviewed. Chapters 4–6 are devoted to the time-frequency analysis, multiresolution analysis, and construction of wavelets. The authors consider semiorthogonal spline wavelets, orthonormal wavelets, and biorthogonal wavelets.

Chapters 7 and 8 present the decomposition and reconstruction algorithms and implement them by a filter bank approach. Ridgelets, curvelets, complex wavelets, and lifting wavelet transforms are introduced too. Finally, Chapters 9 and 10 present numerous applications of wavelets to signal processing (such as edge detection, image compression, and geophysical problems on oilfield industry) and boundary value problems. Chapters 2–10 close with some exercises. Numerous examples and figures are included along with MATLAB programs.

This book provides a thorough treatment of wavelet theory and is very convenient for graduate students and researchers in electrical engineering, physics, and applied mathematics.

[For the first edition (1999) see Zbl 1209.65156.]

Chapters 7 and 8 present the decomposition and reconstruction algorithms and implement them by a filter bank approach. Ridgelets, curvelets, complex wavelets, and lifting wavelet transforms are introduced too. Finally, Chapters 9 and 10 present numerous applications of wavelets to signal processing (such as edge detection, image compression, and geophysical problems on oilfield industry) and boundary value problems. Chapters 2–10 close with some exercises. Numerous examples and figures are included along with MATLAB programs.

This book provides a thorough treatment of wavelet theory and is very convenient for graduate students and researchers in electrical engineering, physics, and applied mathematics.

[For the first edition (1999) see Zbl 1209.65156.]

Reviewer: Manfred Tasche (Rostock)

##### MSC:

65T60 | Numerical methods for wavelets |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

94A11 | Application of orthogonal and other special functions |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |