An "Applications First" Approach to Discrete Wavelet Transformations

Discrete Wavelet Transformations provides readers with a broad elementary introduction to discrete wavelet transformations and their applications. With extensive graphical displays - the book includes over 150 figures - this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image de-noising.

The book begins with an essay that provides a cursory look at wavelet transformation development and illustrates the allure of the tool in digital signal and image applications. A chapter on digital image basics, quantitative and qualitative measures, and Huffman coding provides the reader with the tools necessary to develop a comprehensive understanding of applications. After chapters on Fourier series, convolution, and filtering, the book continues with a development of the Haar wavelet transform and uses it to introduce image compression and image edge detection. The book next presents a development of Daubechies filters and a chapter dedicated to wavelet shrinkage in the area of image and signal denoising. Biorthogonal filters are constructed and the book concludes with a chapter describing their incorporation in the JPEG2000 image comression standard.

The author's "applications first" approach promotes a hands-on treatment of wavelet transformation construction and presents over 400 exercises in a multi-part format that guide readers through the solution to each problem. Over 60 computer labs and software development projects provide opportunities for readers to write modules and experiment with the ideas discussed throughout the text. The author's software package, DiscreteWavelets, is used to perform various imaging and audio tasks, compute wavelet transformations and inverses, and visualize the output of the computations. Supplementary material is also available online and includes an audio and video repository, final project modules, and software for reproducing most examples given in the book. All software, including the DiscreteWavelets package, is available for use with Mathematica®, MATLAB®, and Maple®.

Discrete Wavelet Transformations strongly reinforces the use of mathematics in digital data applications, sharpens programming skills, and provides a foundation for further study of more advanced topics, such as real analysis. This book is ideal for use in an undergraduate course that introduces students to a current topic used in today's digital applications and, at the same time, reinforces concepts covered in calculus and linear algebra. The book also serves as an excellent reference for mathematicians, engineers, and scientists who wish to learn about discrete wavelet transforms at an elementary level.

Reprinted with permission