{"product_id":"discrete-wavelet-transformations-isbn-9781118979273","title":"Discrete Wavelet Transformations","description":"\u003cp\u003e\u003cb\u003eUpdated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe new edition of \u003ci\u003eDiscrete Wavelet Transformations\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eLeveraging 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. \u003c\/p\u003e \u003cp\u003eThe second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eTwo new chapters covering wavelet packets and the lifting method\u003c\/li\u003e \u003cli\u003eA reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques\u003c\/li\u003e \u003cli\u003eA new comprehensive chapter that explains filter derivation using Fourier techniques\u003c\/li\u003e \u003cli\u003eOver 120 examples of which 91 are “live examples,” which allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery\u003c\/li\u003e \u003cli\u003eAn overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented\u003c\/li\u003e \u003cli\u003eA complete rewrite of the \u003ci\u003eDiscreteWavelets\u003c\/i\u003e package called \u003ci\u003eWaveletWare\u003c\/i\u003e for use with Mathematica and MATLAB\u003c\/li\u003e \u003cli\u003eA website, www.stthomas.edu\/wavelets, featuring material containing the \u003ci\u003eWaveletWare\u003c\/i\u003e package, live examples, and computer labs in addition to companion material for teaching a course using the book \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eComprehensive 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.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction: Why Wavelets? 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Vectors and Matrices 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Vectors, Inner Products, and Norms 16\u003c\/p\u003e \u003cp\u003eProblems 21\u003c\/p\u003e \u003cp\u003e2.2 Basic Matrix Theory 23\u003c\/p\u003e \u003cp\u003eProblems 38\u003c\/p\u003e \u003cp\u003e2.3 Block Matrix Arithmetic 40\u003c\/p\u003e \u003cp\u003eProblems 48\u003c\/p\u003e \u003cp\u003e2.4 Convolution and Filters 51\u003c\/p\u003e \u003cp\u003eProblems 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 An Introduction to Digital Images 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Basics of Grayscale Digital Images 70\u003c\/p\u003e \u003cp\u003eProblems 88\u003c\/p\u003e \u003cp\u003eComputer Lab 91\u003c\/p\u003e \u003cp\u003e3.2 Color Images and Color Spaces 91\u003c\/p\u003e \u003cp\u003eProblems 103\u003c\/p\u003e \u003cp\u003eComputer Lab 106\u003c\/p\u003e \u003cp\u003e3.3 Huffman Coding 106\u003c\/p\u003e \u003cp\u003eProblems 113\u003c\/p\u003e \u003cp\u003e3.4 Qualitative and Quantitative Measures 114\u003c\/p\u003e \u003cp\u003eProblems 120\u003c\/p\u003e \u003cp\u003eComputer Labs 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Haar Wavelet Transformation 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Constructing the Haar Wavelet Transformation 127\u003c\/p\u003e \u003cp\u003eProblems 137\u003c\/p\u003e \u003cp\u003eComputer Lab 140\u003c\/p\u003e \u003cp\u003e4.2 Iterating the Process 140\u003c\/p\u003e \u003cp\u003eProblems 146\u003c\/p\u003e \u003cp\u003eComputer Lab 147\u003c\/p\u003e \u003cp\u003e4.3 The Two-Dimensional Haar Wavelet Transformation 147\u003c\/p\u003e \u003cp\u003eProblems 159\u003c\/p\u003e \u003cp\u003eComputer Lab 161\u003c\/p\u003e \u003cp\u003e4.4 Applications: Image Compression and Edge Detection 161\u003c\/p\u003e \u003cp\u003eProblems 177\u003c\/p\u003e \u003cp\u003eComputer Labs 181\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Daubechies Wavelet Transformations 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Daubechies Filter of Length 4 185\u003c\/p\u003e \u003cp\u003eProblems 196\u003c\/p\u003e \u003cp\u003eComputer Lab 203\u003c\/p\u003e \u003cp\u003e5.2 Daubechies Filter of Length 6 203\u003c\/p\u003e \u003cp\u003eProblems 212\u003c\/p\u003e \u003cp\u003eComputer Lab 215\u003c\/p\u003e \u003cp\u003e5.3 Daubechies Filters of Even Length 215\u003c\/p\u003e \u003cp\u003eProblems 225\u003c\/p\u003e \u003cp\u003eComputer Lab 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Wavelet Shrinkage: An Application to Denoising 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 An Overview of Wavelet Shrinkage 232\u003c\/p\u003e \u003cp\u003eProblems 237\u003c\/p\u003e \u003cp\u003eComputer Lab 238\u003c\/p\u003e \u003cp\u003e6.2 VisuShrink 238\u003c\/p\u003e \u003cp\u003eProblems 245\u003c\/p\u003e \u003cp\u003eComputer Lab 246\u003c\/p\u003e \u003cp\u003e6.3 SureShrink 246\u003c\/p\u003e \u003cp\u003eProblems 257\u003c\/p\u003e \u003cp\u003eComputer Labs 260\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Biorthogonal Wavelet Transformations 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The (5; 3) Biorthogonal Spline Filter Pair 262\u003c\/p\u003e \u003cp\u003eProblems 273\u003c\/p\u003e \u003cp\u003eComputer Lab 278\u003c\/p\u003e \u003cp\u003e7.2 The (8; 4) Biorthogonal Spline Filter Pair 278\u003c\/p\u003e \u003cp\u003eProblems 283\u003c\/p\u003e \u003cp\u003eComputer Lab 288\u003c\/p\u003e \u003cp\u003e7.3 Symmetry and Boundary Effects 288\u003c\/p\u003e \u003cp\u003eProblems 307\u003c\/p\u003e \u003cp\u003eComputer Lab 311\u003c\/p\u003e \u003cp\u003e7.4 Image Compression and Image Pansharpening 312\u003c\/p\u003e \u003cp\u003eComputer Lab 320\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Complex Numbers and Fourier Series 321\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Complex Plane and Arithmetic 322\u003c\/p\u003e \u003cp\u003eProblems 332\u003c\/p\u003e \u003cp\u003e8.2 Fourier Series 334\u003c\/p\u003e \u003cp\u003eProblems 344\u003c\/p\u003e \u003cp\u003e8.3 Filters and Convolution in the Fourier Domain 349\u003c\/p\u003e \u003cp\u003eProblems 360\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Filter Construction in the Fourier Domain 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Filter Construction 366\u003c\/p\u003e \u003cp\u003eProblems 377\u003c\/p\u003e \u003cp\u003e9.2 Daubechies Filters 378\u003c\/p\u003e \u003cp\u003eProblems 382\u003c\/p\u003e \u003cp\u003e9.3 Coiflet Filters 382\u003c\/p\u003e \u003cp\u003eProblems 395\u003c\/p\u003e \u003cp\u003e9.4 Biorthogonal Spline Filter Pairs 400\u003c\/p\u003e \u003cp\u003eProblems 410\u003c\/p\u003e \u003cp\u003eComputer Lab 413\u003c\/p\u003e \u003cp\u003e9.5 The Cohen–Daubechies–Feauveau 9\/7 Filter 414\u003c\/p\u003e \u003cp\u003eProblems 423\u003c\/p\u003e \u003cp\u003eComputer Lab 426\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Wavelet Packets 427\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Wavelet Packet Transform 428\u003c\/p\u003e \u003cp\u003eProblems 435\u003c\/p\u003e \u003cp\u003e10.2 Cost Functions and the Best Basis Algorithm 436\u003c\/p\u003e \u003cp\u003eProblems 444\u003c\/p\u003e \u003cp\u003e10.3 The FBI Fingerprint Compression Specification 446\u003c\/p\u003e \u003cp\u003eComputer Lab 460\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Lifting 461\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The LeGall Wavelet Transform 462\u003c\/p\u003e \u003cp\u003eProblems 471\u003c\/p\u003e \u003cp\u003eComputer Lab 473\u003c\/p\u003e \u003cp\u003e11.2 Z–Transforms and Laurent Polynomials 474\u003c\/p\u003e \u003cp\u003eProblems 484\u003c\/p\u003e \u003cp\u003e11.3 A General Construction of the Lifting Method 486\u003c\/p\u003e \u003cp\u003eProblems 499\u003c\/p\u003e \u003cp\u003e11.4 The Lifting Method – Examples 504\u003c\/p\u003e \u003cp\u003eProblems 517\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 The JPEG2000 Image Compression Standard 525\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 An Overview of JPEG 526\u003c\/p\u003e \u003cp\u003eProblems 532\u003c\/p\u003e \u003cp\u003e12.2 The Basic JPEG2000 Algorithm 533\u003c\/p\u003e \u003cp\u003eProblems 539\u003c\/p\u003e \u003cp\u003e12.3 Examples 540\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Basic Statistics 547\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Descriptive Statistics 547\u003c\/p\u003e \u003cp\u003eProblems 549\u003c\/p\u003e \u003cp\u003eA.2 Sample Spaces, Probability, and Random Variables 550\u003c\/p\u003e \u003cp\u003eProblems 553\u003c\/p\u003e \u003cp\u003eA.3 Continuous Distributions 553\u003c\/p\u003e \u003cp\u003eProblems 559\u003c\/p\u003e \u003cp\u003eA.4 Expectation 559\u003c\/p\u003e \u003cp\u003eProblems 565\u003c\/p\u003e \u003cp\u003eA.5 Two Special Distributions 566\u003c\/p\u003e \u003cp\u003eProblems 568\u003c\/p\u003e   \u003cp\u003e\u003cb\u003ePATRICK J. VAN FLEET\u003c\/b\u003e 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.    \u003c\/p\u003e\u003cp\u003e\u003cb\u003eUpdated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eThe new edition of \u003ci\u003eDiscrete Wavelet Transformations\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eLeveraging 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. \u003c\/p\u003e\u003cp\u003eThe second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eTwo new chapters covering wavelet packets and the lifting method\u003c\/li\u003e \u003cli\u003eA reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques\u003c\/li\u003e \u003cli\u003eA new comprehensive chapter that explains filter derivation using Fourier techniques\u003c\/li\u003e \u003cli\u003eOver 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\u003c\/li\u003e \u003cli\u003eAn overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented\u003c\/li\u003e \u003cli\u003eA complete rewrite of the \u003ci\u003eDiscreteWavelets\u003c\/i\u003e package called \u003ci\u003eWaveletWare\u003c\/i\u003e for use with Mathematica and MATLAB\u003c\/li\u003e \u003cli\u003eA website, www.stthomas.edu\/wavelets, featuring material containing the \u003ci\u003eWaveletWare\u003c\/i\u003e package, live examples, and computer labs in addition to companion material for teaching a course using the book\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eComprehensive 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989075116261,"sku":"NP9781118979273","price":128.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118979273.jpg?v=1761782692","url":"https:\/\/k12savings.com\/products\/discrete-wavelet-transformations-isbn-9781118979273","provider":"K12savings","version":"1.0","type":"link"}