Discrete Wavelet Transformations (eBook)

An Elementary Approach with Applications

Patrick Van Fleet (Autor)

eBook Download: PDF

2011 | 1. Auflage
564 Seiten
John Wiley & Sons (Verlag)
9781118030660 (ISBN)

Infos

An "applications first" approach to discrete wavelettransformations

Discrete Wavelet Transformations provides readers with a broadelementary introduction to discrete wavelet transformations andtheir applications. With extensive graphical displays, thisself-contained book integrates concepts from calculus and linearalgebra into the construction of wavelet transformations and theirvarious applications, including data compression, edge detection inimages, and signal and image denoising.

The book begins with a cursory look at wavelet transformationdevelopment and illustrates its allure in digital signal and imageapplications. Next, a chapter on digital image basics, quantitativeand qualitative measures, and Huffman coding equips readers withthe tools necessary to develop a comprehensive understanding of theapplications. Subsequent chapters discuss the Fourier series,convolution, and filtering, as well as the Haar wavelet transformto introduce image compression and image edge detection. Thedevelopment of Daubechies filtersis presented in addition tocoverage of wavelet shrinkage in the area of image and signaldenoising. The book concludes with the construction of biorthogonalfilters and also describes their incorporation in the JPEG2000image compression standard.

The author's "applications first" approach promotes a hands-ontreatment of wavelet transforma-tion construction, and over 400exercises are presented in a multi-part format that guide readersthrough the solution to each problem. Over sixty computer labs andsoftware development projects provide opportunities for readers towrite modules and experiment with the ideas discussed throughoutthe text. The author's software package, DiscreteWavelets, is usedto perform various imaging and audio tasks, compute wavelettransformations and inverses, and visualize the output of thecomputations. Supplementary material is also available via thebook's related Web site, which includes an audio and videorepository, final project modules, and softwarefor reproducingexamples from the book. All software, including theDiscreteWavelets package, is available for use withMathematica®, MATLAB®, and Maple.

Discrete Wavelet Transformations strongly reinforces the use ofmathematics in digital data applications, sharpens programmingskills, and provides a foundation for further study of moreadvanced topics, such as real analysis. This book is ideal forcourses on discrete wavelet transforms and their applications atthe undergraduate level and also serves as an excellent referencefor mathematicians, engineers, and scientists who wish to learnabout discrete wavelet transforms at an elementary level.

Autor

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.

Inhalt

Preface

Acknowledgements
* Introduction: Why Wavelets
* Vectors and Matrices
* An Introduction to Digital Images
* Complex Numbers and Fourier Series
* Convolution and Filters
* The Haar Wavelet Transformation
* Daubechies Wavelet Transformations
* Orthogonality and Fourier Series
* Wavelet Shrinkage: An Application to Denoising
* Biorthogonal Filters
* Computing Biorthogonal Wavelet Transformations
* The JPEG2000 Image Compression Standard

Appendix A: Basic Statistics

References

Index

Rezensionen

"The book is a valuable reference for wavelet applications and the theory of underlying 2-band filterbanks." (Mathematical Reviews, Issue 2009g)

Produkt-Details

• Erscheint lt. Verlag: 1.3.2011
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: Angewandte Mathematik • Applied mathematics • Diskrete Mathematik • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Mathematics • Mathematik • Signal Processing • Signalverarbeitung • Wavelets
• ISBN-13: 9781118030660 / 9781118030660