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Informationen zum Autor PATRICK J. VAN FLEET is Professor and Chair of the Department of Mathematics at the University of St. Thomas in St. Paul, Minnesota. He has authored several journal articles on (multi)wavelets and conducted sponsored workshops for developing and teaching an applications-first course on wavelets. He received his PhD in Mathematics from Southern Illinois University-Carbondale in 1991. Klappentext Updated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals The new edition of Discrete Wavelet Transformations continues to guide readers through the abstract concepts of wavelet theory by using Dr. Van Fleet's highly practical, application-based approach, which reflects how mathematicians construct solutions to challenges outside the classroom. By introducing the Haar, orthogonal, and biorthogonal filters without the use of Fourier series, Van Fleet allows his audience to connect concepts directly to real-world applications at an earlier point than other publications in the field. Leveraging extensive graphical displays, this self-contained volume integrates concepts from calculus and linear algebra into the constructions of wavelet transformations and their applications, including data compression, edge detection in images, and denoising of signals. Conceptual understanding is reinforced with over 500 detailed exercises and 24 computer labs. The second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include: Two new chapters covering wavelet packets and the lifting method A reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques A new comprehensive chapter that explains filter derivation using Fourier techniques Over 120 examples of which 91 are "live examples," that allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery An overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented A complete rewrite of the DiscreteWavelets package called WaveletWare for use with Mathematica and MATLAB A website, www.stthomas.edu/wavelets, featuring material containing the WaveletWare package, live examples, and computer labs in addition to companion material for teaching a course using the book Comprehensive and grounded, this book and its online components provide an excellent foundation for developing undergraduate courses as well as a valuable resource for mathematicians, signal process engineers, and other professionals seeking to understand the practical applications of discrete wavelet transformations in solving real-world challenges. Inhaltsverzeichnis 1 Introduction: Why Wavelets? 1 2 Vectors and Matrices 15 2.1 Vectors, Inner Products, and Norms 16 Problems 21 2.2 Basic Matrix Theory 23 Problems 38 2.3 Block Matrix Arithmetic 40 Problems 48 2.4 Convolution and Filters 51 Problems 65 3 An Introduction to Digital Images 69 3.1 The Basics of Grayscale Digital Images 70 Problems 88 Computer Lab 91 3.2 Color Images and Color Spaces 91 Problems 103 Computer Lab 106 3.3 Huffman Coding 106 Problems 113 3.4 Qualitative and Quantitative Measures 114 Problems 120 Computer Labs 123 4 The Haar Wavelet Transformation 125 4.1 Constructing the Haar Wavelet Transformation 127 Problems 137 Computer Lab 140 4.2 Iterating the Process 140 Problems 146 Computer Lab 147 4.3 The Two-Dimensional Haar Wavelet Transformation 147 Problems 159 Computer...
