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Chui C.K. — Wavelets: a mathematical tool for signal processing
Chui C.K. — Wavelets: a mathematical tool for signal processing

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Название: Wavelets: a mathematical tool for signal processing

Автор: Chui C.K.

Аннотация:

Wavelets continue to be powerful mathematical tools that can be used to solve problems for which the Fourier (spectral) method does not perform well or cannot handle. This book is for engineers, applied mathematicians, and other scientists who want to learn about using wavelets to analyze, process, and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. The only mathematically rigorous monograph written by a mathematician specifically for nonspecialists, it describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches, and provides information for problem solving, putting the reader at the forefront of current research. Written for an interdisciplinary audience of engineers, applied mathematicians, and other scientists with little or no knowledge of wavelets, readers with an undergraduate background in applied mathematics or engineering will appreciate this book.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 229

Добавлена в каталог: 05.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l^2$ sequence norm      41
$L^2$-closure      9 40
$L^2$-norm      5
$L^2$-projection      42
Acoustic signal      37 161
Analog filters      23
Analog representation      92 119—121
Analog signal      21 45
Analyzing wavelet      11 34 92
Arithmetic coding      175—176
Asymmetry      81
Asymptotically optimal      52 90 116 131
Audio compression      177
Audio perception      177
Autocorrelation function      98 126
Autoregressive—moving average (ARMA)      50 109
B-frame      181
B-splines      52 119 184
B-splines cardinal      48 76 130 170 184
B-splines cardinal dual      57
B-splines normalized      140
B-wavelets      119 184
Backward difference operation      124
Bandlimited signals      24 39 66 105
Bandpass filter      10—11 102 166 185
Bandpass filter function      26
Bandpass window function      34 59 93
Bandwidth      11 24
Bandwidth RMS      27—28
Battle — Lemaire scaling functions      71
Battle — Lemaire wavelets      71—73
Biorthogonal wavelets      89
Blur      51 66 119
Boundary B-splines      144
Boundary cubic B-wavelets      157—160
Boundary linear B-wavelets      153 156
Boundary spline wavelets      145
Butterworth filter      30 53
Calderon      1
Calibration constant      35—36
Cardinal B-splines      48 76 130 170 184
Cardinal B-wavelets      97 102
Cardinal dual B-splines      56
cardinal splines      52 75—78 121 127
Center      27—28 104 139
Centered IWT      36—37
Centered STFT      31
Change of bases      94 111 130 184
Characteristic function      24
Chirp signal      32—33
Chrominancy      179
Cochlea      37—38
Codebook      174
Codeword      174
Coding arithmetic      175—176
Coding entropy      173
Coding Huffman      175—176
Coding subband      1 20
Compact support      56 94 139
Complete oscillation      117
Complex conjugation      10 108
Compression audio      177
Compression data      131 171 177
Compression scheme      171
Compression video      180
Continuous wavelet transform (CWT)      11 32 59 133
Convolution      25 37
Corner smoothing functions      66—67
Corti      37
Cowlets      117 165
Data compression      131 171 177
Daubechies scaling functions      77—78 81—83 86
Daubechies wavelets      60 77 81 97
Decoding      175
Decomposition algorithm      19 109 128
Decomposition matrices      127
Decomposition relations      63 108
Decomposition sequences      108
Decompression      177
Dequantization      177
Detection      161 165—166
Detection procedure      166
Diagonally dominant matrix portion      186
Difference equations      161
Difference image      180
Direct-sum      10 91
Direct-sum decomposition      91
Discontinuity      161
discrete wavelet transform (DWT)      11 134 162
Divided differences      140 142
Downsampling      20 128 164 167
Drum scanner      178
Dual B-spline series      166—167
Dual B-splines      57 166 171
Dual B-wavelets      152
Dual bases      129
Dual scalar function      171
Dual wavelets      90 107 134 171
Duality principle      90 105 129
Duals      44 90 106
Embedded zero tree (EZW)      173
Entropy coding      173
Errors      41 120
Euler — Frobenius Laurent (E—F L) polynomial      71—72 94
Euler — Frobenius Laurent (E—F L) series      94
Fast algorithms      17
Fast Fourier transform (FFT)      16 132 178
Feature extraction      161
Filter banks      18 22 178
Filter characteristic      65
Filter length      81
Forward difference operation      124
Fourier series      45 68
Fourier transform      24 61 132
Fredholm integral equation      183
Frequency center      29
Frequency window      32 34 93
Functions autocorrelation      98 126
Functions corner smoothing      66—67
Functions Gaussian      28—29 31 114
Functions Green's      188
Functions transfer      25 37—38 81
Fundamental cardinal interpolating splines      72 120
Fundamental interpolating splines      72
Gabor      31
Gabor transform      31
Gaussian functions      28—29 31 114
Gramian matrices      125—127
Graphical display      131
Green's function      188
Haar scaling function      7 8 48
Haar wavelet      7—10 63 97
Hermitian      125 127
Hertz (Hz)      10 24 35
High-frequency components      135
Hilbert space      125 127 140
histogram      172
Huffman binary tree      176
Huffman coding      175—176
I-frame      181
Ideal bandpass filters      25—27 65
Ideal lowpass filters      24 27 29
Image medical      178 182
Image monochrome      178
Image still      178
Inner product      27 32
Integral equation      161 182
Integral equation Fredholm      183
Integral equation Volterra      183
Integral equation Weiner — Hopf      183
Integral operator      183
Integral wavelet transform (IWT)      32 33—34 92
Interior      150
Interior B-splines      144
Interior cubic B-wavelet      158—159
Interior knots      143
Interior linear B-wavelet      153—156
Interior scaling functions      146
Interpolation      120
Inverse Fourier transform      24—25 68 183
Isolated singularities      162
Kernel      182
Knot      67
Knot sequence      75—76 143
Kronecker delta symbol      9 44 163
Laplacian distribution      173
Laser      178
Laurent polynomial      101
Linear filters      37
Linear phase      184
Localness      47
Lossy transformation      172
Low-frequency components      66
Lowpass filter      11 95
Lowpass window      30 40
Luminancy      179
Masking property      177
Maxima side-lobe/main-lobe ratios      85
Measurable      23—24
Medical image      178 182
Message      174
Method of moment (MoM)      183
Meyer scaling functions      66
Meyer wavelets      66
Minimum support      101 116
Minimum-phase digital filtering      81
Monochrome image      178
MPEG      177 181
MPEG-I      177
Multidimensional wavelet      133 168
Multidimensional wavelet transform      168
Multifrequency      134
Multigrid method      187
Multiresolution analysis (MRA)      39 49 90 182
Music data      12—16 162
MUSICAM      177—178
Nested property      7 51 96
Nonreversible transformation      172
Normalization constants      21 76
Normalized B-splines      140
NTSC color space      179
Octave      10 60
One-side center      34
One-side radius      34
Optimal scalar function      173
Order of approximation      59 177
Orthogonal analysis      59
Orthogonal decomposition and reconstruction      124
Orthogonal projection      42 120 168
Orthogonal wavelet      60
Orthonormal basis      44 63
Orthonormal family      44 77
Orthonormal wavelet      63 89 97
Orthonormalization process      62 72 93
P-frame      181
Parseval's identity      29 31
Partial differential equation (PDE)      182
Partition of RMS bandwidths      137
Peak signal-to-noise ratio (PSNR)      180
Petrov — Galerkin method      185
Phase shift      30
Piecewise constant interpolation      39 47
Piecewise continuous      23
Poly a frequency (PF)      115
Polynomials      56 78 98
Pop noise      16 162
Probabilities      175
Quantization      177
Quantization noise      177
Quantization scheme      173
Quantizer      172
Quasi interpolation      124 166
RADIUS      28—29
Real line      23
Reciprocal polynomial      80
Reconstruction algorithm      20 109 128
Reconstruction sequences      86 109
Restriction      56 134 144
Resultant equation      185
RGB color image      179
Riesz basis      9 41—42 61
Riesz bounds      41—42
Riesz lemma      80
Rms bandwidth      28—30 50 95
RMS finite      39
Root Mean Square (RMS)      27—30 105
Root mean square error (RMSE)      180
Sampling operator      42
Sampling period      40 49
Sampling theorem      39—40
Scale parameter      32—33
Scaling functions      45—46 69 95 179
Segmentations      4 7 182
Seismic block      182
Semiorthogonal spline wavelet      183
Semiorthogonal wavelets      97 105 110
Shannon sampling function      25 40 96
Shannon wavelet      64 97
Shift variance      162 164
Short-time Fourier transform (STFT)      30—31 96
Side-lobe/main-lobe power ratios      53 85—86
Signal matching      10
Signal representation      119 131
Signal spaces      39—40
Sinusoidal      16 36 162
Solid-state camera      178
sparse      89
Sparsity      187
Spatial redundancy      180
Spectral analysis      177
Spectral redundancy      161 180
Spectrum      31 95
Spline spaces      77 166
Spline wavelet      71 97
Spreading function      177
Stability      40—41 123
Stable basis      41
Staircase      172
Statistical scheme      175
Step size      173 177
Still image      178
Stoplets      116—117
Stromberg wavelets      75 77
Subband Coding      20
Support      48
Symbol      72
Symmetry      116
Synthesizing wavelet      93
Taylor expansion      139 161
Temporal redundancy      180
Tensor product      134 168
Thresholding      168 171
Thresholding parameter      172 173
Thresholding scheme      173
Time localization      27—28 47 96
Time-frequency analysis      8 11
Time-frequency windows      23 96 113
Time-window      27—33 47 93
TM plane wave      188
Toeplitz kernel      115
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