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出版社:世界圖書出版公司
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ISBN:9787510037610
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作者:(美)瓦爾納
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頁數:449
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出版日期:2011-07-01
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印刷日期:2011-07-01
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包裝:平裝
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開本:24開
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版次:1
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印次:1
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瓦爾納編著的《小波分析導論(英文影印版)》是一部全面講述小波分析理論的基礎教程,主要內容包括小波基的構造和分析。通過詳細講述哈爾級數展開了小波理論中心思想的討論,進而運用*加抽像的方法講述哈爾級數,*深層次的講述了哈爾結構的變化和擴展。目次:(**部分)基礎:函數和收斂;傅裡葉級數;傅裡葉變換;信號和繫統;(第二部分)哈爾繫統:離散哈爾變換;(第三部分)正交小波基:光滑、緊支撐小波包;(第四部分)其他小波結構:雙正交小波;小波包;(第五部分)應用:圖像壓縮;積分算子。附錄。
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preface Ⅰ preliminaries 1 functions and convergence 1.1 functions 1.1.1 bounded (l∞) functions 1.1.2 integrable (l1) functions 1.1.3 square integrable (l2) functions 1.1.4 differentiable (cn) functions 1.2 convergence of sequences of functions 1.2.1 numerical convergence 1.2.2 pointwise convergence 1.2.3 uniform (l∞) convergence 1.2.4 mean (ll) convergence 1.2.5 mean-square (l2) convergence 1.2.6 interchange of limits and integrals 2 fourier series 2.1 trigonometric series 2.1.1 periodic functions 2.1.2 the trigonometric system 2.1.3 the fourier coefficients 2.1.4 convergence of fourier series 2.2 approximate identities 2.2.1 motivation from fourier series 2.2.2 definition and examples 2.2.3 convergence theorems 2.3 generalized fourier series 2.3.1 orthogonality 2.3.2 generalized fourier series 2.3.3 completeness 3 the fourier transform 3.1 motivation and definition 3.2 basic properties of the fourier transform 3.3 fourier inversion 3.4 convolution 3.5 plancherel's formula 3.6 the fourier transform for l2 functions 3.7 smoothness versus decay 3.8 dilation, translation, and modulation 3.9 bandlimited functions and the sampling formula 4 signals and systems 4.1 signals 4.2 systems 4.2.1 causality and stability 4.3 periodic signals and the discrete fourier transform 4.3.1 the discrete fourier transform 4.4 the fast fourier transform 4.5 l2 fourier series Ⅱ the haar system 5 the haar system 5.1 dyadic step functions 5.1.1 the dyadic intervals 5.1.2 the scale j dyadic step functions 5.2 the haar system 5.2.1 the haar scaling functions and the haar functions. 5.2.2 orthogonality of the haar system 5.2.3 the splitting lemma 5.3 haar bases on [0, 1] 5.4 comparison of haar series with fourier series 5.4.1 representation of functions with small support 5.4.2 behavior of haar coefficients near jump discontinuities 5.4.3 haar coefficients and global smoothness 5.5 haar bases on r 5.5.1 the approximation and detail operators 5.5.2 the scale j haar system on r 5.5.3 the hair system on r 6 the discrete haar transform 6.1 motivation 6.1.1 the discrete haar transform (dht) 6.2 the dht in two dimensions 6.2.1 the row-wise and column-wise approximations and details 6.2.2 the dht for matrices 6.3 image analysis with the dht 6.3.1 approximation and blurring 6.3.2 horizontal, vertical, and diagonal edges 6.3.3 "naive" image compression Ⅲ orthonormal wavelet bases 7 multiresolution analysis 7.1 orthonormal systems of translates 7.2 definition of multiresolution analysis 7.2.1 some basic properties of mras 7.3 examples of multiresolution analysis 7.3.1 the haar mra 7.3.2 the piecewise linear mra 7.3.3 the bandlimited mra 7.3.4 the meyer mra 7.4 construction and examples of orthonormal wavelet bases 7.4.1 examples of wavelet bases 7.4.2 wavelets in two dimensions 7.4.3 localization of wavelet bases 7.5 proof of theorem 7.35 7.5.1 sufficient conditions for a wavelet basis 7.5.2 proof of theorem 7.35 7.6 necessary properties of the scaling function 7.7 general spline wavelets 7.7.1 basic properties of spline functions 7.7.2 spline multiresolution analyses 8 the discrete wavelet transform 8.1 motivation: from mra to a discrete transform 8.2 the quadrature mirror filter conditions 8.2.1 motivation from mra 8.2.2 the approximation and detail operators and their adjoints 8.2.3 the quadrature mirror filter (qmf) conditions 8.3 the discrete wavelet transform (dwt) 8.3.1 the dwt for signals 8.3.2 the dwt for finite signals 8.3.3 the dwt as an orthogonal transformation 8.4 scaling functions from scaling sequences 8.4.1 the infinite product formula 8.4.2 the cascade algorithm 8.4.3 the support of the scaling function 9 smooth, compactly supported wavelets 9.1 vanishing moments 9.1.1 vanishing moments and smoothness 9.1.2 vanishing moments and approximation 9.1.3 vanishing moments and the reproduction of polynomials 9.1.4 equivalent conditions for vanishing moments 9.2 the daubechies wavelets 9.2.1 the daubechies polynomials 9.2.2 spectral factorization 9.3 image analysis with smooth wavelets 9.3.1 approximation and blurring 9.3.2 "naive" image compression with smooth wavelets Ⅳ other wavelet constructions 10 biorthogonal wavelets 10.1 linear independence and biorthogonality 10.2 riesz bases and the frame condition 10.3 riesz bases of translates 10.4 generalized multiresolution analysis (gmra) 10.4.1 basic properties of gmra 10.4.2 dual gmra and riesz bases of wavelets 10.5 riesz bases orthogonal across scales 10.5.1 example: the piecewise linear gmra 10.6 a discrete transform for biorthogonal wavelets 10.6.1 motivation from gmra 10.6.2 the qmf conditions 10.7 compactly supported biorthogonal wavelets 10.7.1 compactly supported spline wavelets 10.7.2 symmetric biorthogonal wavelets 10.7.3 using symmetry in the dwt 11 wavelet packets 11.1 motivation: completing the wavelet tree 11.2 localization of wavelet packets 11.2.1 time/spatial localization 11.2.2 frequency localization 11.3 0rthogonality and completeness properties of wavelet packets 11.3.1 wavelet packet bases with a fixed scale 11.3.2 wavelet packets with mixed scales 11.4 the discrete wavelet packet transform (dwpt) 11.4.1 the dwpt for signals 11.4.2 the dwpt for finite signals 11.5 the best-basis algorithm 11.5.1 the discrete wavelet packet library 11.5.2 the idea of the best basis 11.5.3 description of the algorithm Ⅴ applications 12 image compression 12.1 the transform step 12.1.1 wavelets or wavelet packets? 12.1.2 choosing a filter 12.2 the quantization step 12.3 the coding step 12.3.1 sources and codes 12.3.2 entropy and information 12.3.3 coding and compression 12.4 the binary huffman code 12.5 a model wavelet transform image coder 12.5.1 examples 13 integral operators 13.1 examples of integral operators 13.1.1 sturm-liouville boundary value problems 13.1.2 the hilbert transform 13.1.3 the radon transform 13.2 the bcr algorithm 13.2.1 the scale j approximation to t 13.2.2 description of the algorithm Ⅵ appendixes a review of advanced calculus and linear algebra a.1 glossary of basic terms from advanced calculus and linear algebra a.2 basic theorems from advanced calculus b excursions in wavelet theory b.1 other wavelet constructions b.1.1 m-band wavelets b.1.2 wavelets with rational noninteger dilation factors b.1.3 local cosine bases b.1.4 the continuous wavelet transform b.1.5 non~mra wavelets b.1.6 multiwavelets b.2 wavelets in other domains b.2.1 wavelets on intervals b.2.2' wavelets in higher dimensions b.2.3 the lifting scheme b.3 applications of wavelets b.3.1 wavelet denoising b.3.2 multiscale edge detection b.3.3 the fbi fingerprint compression standard c references cited in the text index
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