Discrete Wavelet Transformations
An Elementary Approach with Applications
By (author) Patrick J. Van Fleet
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Discrete Wavelet Transformations by Patrick J. Van Fleet
Book DescriptionAn "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, 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 denoising. The book begins with a cursory look at wavelet transformation development and illustrates its allure in digital signal and image applications. Next, a chapter on digital image basics, quantitative and qualitative measures, and Huffman coding equips readers with the tools necessary to develop a comprehensive understanding of the applications. Subsequent chapters discuss the Fourier series, convolution, and filtering, as well as the Haar wavelet transform to introduce image compression and image edge detection. The development of Daubechies filtersis presented in addition to coverage of wavelet shrinkage in the area of image and signal denoising. The book concludes with the construction of biorthogonal filters and also describes their incorporation in the JPEG2000 image compression standard. The author's "applications first" approach promotes a hands-on treatment of wavelet transforma-tion construction, and over 400 exercises are presented in a multi-part format that guide readers through the solution to each problem. Over sixty 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 via the book's related Web site, which includes an audio and video repository, final project modules, and softwarefor reproducing examples from the book. All software, including the DiscreteWavelets package, is available for use with Mathematica(r), MATLAB(r), 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 courses on discrete wavelet transforms and their applications at the undergraduate level and also serves as an excellent reference for mathematicians, engineers, and scientists who wish to learn about discrete wavelet transforms at an elementary level.
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Book DetailsISBN: 9780470183113
(237mm x 162mm x 32mm)
Publisher: John Wiley and Sons Ltd
Publish Date: 1-Feb-2008
Country of Publication: United States
Books By Author Patrick J. Van Fleet
Wavelet Theory, Hardback (November 2009)» View all books by Patrick J. Van Fleet
This self-contained, elementary introduction to wavelet theory and its applications provides a comprehensive treatment of the topic using two real-life applications: the FBI Wavelet Scalar Quantization Standard and image segmentation. Over 400 exercises plus extensive details and examples help readers gain a full understanding of the material.
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Author Biography - Patrick J. Van Fleet
Patrick J. Van Fleet, PhD, is Professor of Mathematics and Director of the Center for Applied Mathematics in the Mathematics Department at the University of St. Thomas in St. Paul, Minnesota. He is the author of several journal articles in his areas of research interest, which include wavelets, multiwavelets, and problems in spline theory. Dr. Van Fleet has been an invited lecturer at many seminars, colloquia, and professional meetings, and he has conducted several workshops for faculty interested in teaching a course on wavelets and their applications.
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