Discrete wavelet transform. A signal processing approach. (English) Zbl 1327.94001
Hoboken, NJ: John Wiley & Sons (ISBN 978-1-119-04606-6/hbk). xi, 323 p. (2015).
This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing. The DWT is presented by the author from a digital signal processing point of view. This book is mainly written for broad readership of graduate students and researchers in physics, computer science, and engineering with special interest in digital signal and image processing. The author demonstrates clearly the properties of the DWT by numerous examples and figures. All computations can be realized by MATLAB programs available at the website of this book.
The contents of this textbook is divided into three parts. The first part (with Chapters 2 – 7) has preliminary character and presents the essentials of digital signal processing (such as operations of discrete signals, convolution and correlation, Fourier analysis of discrete signals, \(z\)-transforms of discrete signals, finite impulse response (FIR) filters, and multirate digital signal processing).
The core of the book is the second part (with Chapters 8 – 14) which presents the theory of the DWT and some extended wavelet transforms. Since most of the concepts of the DWT are easy to understand by studying the Haar DWT, the author describes the Haar DWT first. Then some orthogonal DWT’s (such as Daubechies filters of length 4 and Coiflet filters of length 6) are designed. The often used biorthogonal DWT’s are presented too. Some implementation aspects of the DWT using typical filters are discussed. As extensions of DWT the author describes the discrete wavelet packet transform, discrete stationary wavelet transform, and dual-tree DWT. The dual-tree DWT provides good directional selectivity and is nearly shift-invariant.
In the last part (with Chapters 15 – 16), two of the major applications of the DWT are presented. The image compression of digital images (with short description of the image compression standard JPEG 2000) and signal denoising are examined.
Each chapter ends with a short summary and many exercises. Answers of selected exercises are given too. Doubtless, this nice book will stimulate the practical education in the theory of DWT and its applications.
The contents of this textbook is divided into three parts. The first part (with Chapters 2 – 7) has preliminary character and presents the essentials of digital signal processing (such as operations of discrete signals, convolution and correlation, Fourier analysis of discrete signals, \(z\)-transforms of discrete signals, finite impulse response (FIR) filters, and multirate digital signal processing).
The core of the book is the second part (with Chapters 8 – 14) which presents the theory of the DWT and some extended wavelet transforms. Since most of the concepts of the DWT are easy to understand by studying the Haar DWT, the author describes the Haar DWT first. Then some orthogonal DWT’s (such as Daubechies filters of length 4 and Coiflet filters of length 6) are designed. The often used biorthogonal DWT’s are presented too. Some implementation aspects of the DWT using typical filters are discussed. As extensions of DWT the author describes the discrete wavelet packet transform, discrete stationary wavelet transform, and dual-tree DWT. The dual-tree DWT provides good directional selectivity and is nearly shift-invariant.
In the last part (with Chapters 15 – 16), two of the major applications of the DWT are presented. The image compression of digital images (with short description of the image compression standard JPEG 2000) and signal denoising are examined.
Each chapter ends with a short summary and many exercises. Answers of selected exercises are given too. Doubtless, this nice book will stimulate the practical education in the theory of DWT and its applications.
Reviewer: Manfred Tasche (Rostock)
MSC:
| 94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 65T60 | Numerical methods for wavelets |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
