Quaternion and Clifford Fourier Transforms and Wavelets / edited by Eckhard Hitzer, Stephen J. Sangwine
(Trends in Mathematics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Basel : Springer Basel : Imprint: Birkhäuser |
| 出版年 | 2013 |
| 本文言語 | 英語 |
| 大きさ | XXVII, 338 p : online resource |
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| 内容注記 | Preface History of Quaternion and Clifford-Fourier Transforms and Wavelets Part I: Quaternions 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions 5 Bochner’s Theorems in the Framework of Quaternion Analysis 6 Bochner-Minlos Theorem and Quaternion Fourier Transform Part II: Clifford Algebra 7 Square Roots of -1 in Real Clifford Algebras 8 A General Geometric Fourier Transform 9 Clifford-Fourier Transform and Spinor Representation of Images 10 Analytic Video (2D+t) Signals Using Clifford-Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras 11 Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications 12 Color Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising 13 Seeing the Invisible and Maxwell’s Equations 14 A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl_{0,n} 15 The Balian-Low theorem for the Windowed Clifford-Fourier Transform 16 Sparse Representation of Signals in Hardy Space. - Index |
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| 一般注記 | Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers |
| 著者標目 | Hitzer, Eckhard editor Sangwine, Stephen J. editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Image processing LCSH:Matrix theory LCSH:Algebra LCSH:Fourier analysis LCSH:Numerical analysis LCSH:Number theory FREE:Mathematics FREE:Number Theory FREE:Linear and Multilinear Algebras, Matrix Theory FREE:Numerical Analysis FREE:Fourier Analysis FREE:Image Processing and Computer Vision |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9783034806039 
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| ISBN | 9783034806039 |
| URL | http://dx.doi.org/10.1007/978-3-0348-0603-9 |
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