000			04599nam a22005415i 4500
001			978-3-0348-0603-9
003			DE-He213
005			20140220082836.0
007			cr nn 008mamaa
008			130625s2013 sz | s |||| 0|eng d
020			_a9783034806039 _9978-3-0348-0603-9
024	7		_a10.1007/978-3-0348-0603-9 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aHitzer, Eckhard. _eeditor.
245	1	0	_aQuaternion and Clifford Fourier Transforms and Wavelets _h[electronic resource] / _cedited by Eckhard Hitzer, Stephen J. Sangwine.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2013.
300			_aXXVII, 338 p. 76 illus., 44 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aTrends in Mathematics
505	0		_aPreface.- 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.
520			_aQuaternion 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.
650		0	_aMathematics.
650		0	_aComputer vision.
650		0	_aMatrix theory.
650		0	_aFourier analysis.
650		0	_aNumerical analysis.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aNumerical Analysis.
650	2	4	_aFourier Analysis.
650	2	4	_aImage Processing and Computer Vision.
700	1		_aSangwine, Stephen J. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034806022
830		0	_aTrends in Mathematics
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0603-9
912			_aZDB-2-SMA
999			_c96314 _d96314