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Hubbard B. — The World According to Wavelets: The Story of a Mathematical Technique in the Making
Hubbard B. — The World According to Wavelets: The Story of a Mathematical Technique in the Making



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Íàçâàíèå: The World According to Wavelets: The Story of a Mathematical Technique in the Making

Àâòîð: Hubbard B.

Àííîòàöèÿ:

I own the very first (French) edition of Mrs. Barbara's book.

It is nice reading, but not so fun as some would say.

It has some advanced calculus level math ( Fourier transform ) and treats mainly Haar wavelets.

As an introduction to the subject it is quite adequate, but if you need/want something more go elsewhere.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1996

Êîëè÷åñòâî ñòðàíèö: 275

Äîáàâëåíà â êàòàëîã: 26.04.2014

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
"Hat" notation      96 103
$L^{2}$ (space)      133 168 176—177 185
Adaptive time segmentation      78—80
Adaptive windowed Fourier analysis      see "Malvar wavelets"
Adelson, Edward      42 45 47 62—63 139 162 187 188 192—193
Alessandro      see "d'Alessandro Christophe"
Amplitude      99
Analog      18
Analytical Theory of Heat      7—8 14—15
Apery, Roger, and zeta function      184
Argoul, F.      54
Arneodo, Alain      54 55 59
Arnold, Vladimir, and KAM theorem      113
Artifacts      141 197
Artifacts, danger of, with wavelets      55—56 61
Artifacts, motion, reduction of, using wavelets      53—54
Astronomy      54 125
Atomic decompositions      26
Balian, Roger      29 36 78
Banach, Stefan      182
Barlaud, Michel      69—70
Basis      56 127—128 232—233 see
Battle — Lemarie spline functions      45 164
Battle, Guy      36 45
Benzi, Roberto      56
Berger, Jonathan      84
Best basis      81—86 88 136 194 201 202 205—207
Beylkin, Gregory      61 70
Bijaoui, Albert      54
Biorthogonal wavelets      69 80 196—197
Biot, Jean-Baptiste      109
Birkhoff, George      113
Bishop, Peter      187
Bit      64
Brahms      3 83—84
Burt, Peter      42 45 47 139 162
BYTE      64
Calderon, A.P.      186
Cayley, Arthur      122
Chameleon effect      55
Chaos      11 46
Ciliberto, S.      56
Coefficients      30 see "Wavelet
Coefficients, computing in non-orthogonal basis      133—135
Coefficients, computing in orthonormal basis      126 129—133
Coefficients, computing with integrals      30—33 98 114—116 126 131—133
Coefficients, filter coefficients      159
Cohen, Albert      78
Coherent structures      72
Coifman, Ronald      3 36 75 77—78 85
Coifman, Ronald, Best Basis (including Brahms)      81 83—84
Coifman, Ronald, fast algorithms      40
Coifman, Ronald, matrix compression      70—71
Compact support      45 47 48 140 161
Compact transforms      189 190
Complex conjugate      136 226 232
Complex exponential      102
complex numbers      101—102 214—215
Complex-valued vectors, scalar product of      136
Complex-valued wavelets      75
Compression      64—65 67—68 78 162 188—189 198 203 see
Compression, comparing methods difficult      70
Compression, matrices      70—71
Compression, most signals not compressible      67
Compression, random signal incompressible      65—67
Compression, wavelets and      33 63 68—71 83
Computers      18 20 26 29 46 72 74—75 117 123 192—193
Constant Q filtering      62
Continuous wavelet transform      34—36 61 74—75 80 81 124—125 126 196
Continuous wavelet transform, aesthetics of      74
Continuous wavelet transform, formula and fast algorithms      124—125
Convergence      104—113
Convergence, easier proof of convergence of Fourier series      106 232—235
Convergence, pointwise      106
Convergence, Siegel, Carl, and small divisor problem      109
Convergence, small divisors and stability of solar system      107—113
Convergence, uniform      106
Convergence, weak      229
Convolutions, definition      157—158
Convolutions, wavelet transform and      158—161
Cooley, J.W.      117
Correlation      32 81—82
Cosine      212
Cousin, V.      5 6
Critical sampling      34 193
Crossword puzzles      82
D'Alembert      11
d'Alessandro, Christophe      80 203
Daubechies wavelets      45—48 149 163 194 195 203
Daubechies, Ingrid, compression and wavelets      63 68—69 196
Daubechies, Ingrid, early involvement with wavelets      45 47
Daubechies, Ingrid, fast wavelet transform      155
Daubechies, Ingrid, matrix compression      71
Daubechies, Ingrid, multiresolution      39
Daubechies, Ingrid, noise      52
Daubechies, Ingrid, notation      142
Daubechies, Ingrid, pure mathematics and wavelets      52
Daubechies, Ingrid, quantization      69 134—135
Daubechies, Ingrid, redundance      36
Daubechies, Ingrid, time-frequency decompositions with wavelets      48—49
Daubechies, Ingrid, vanishing moments      161 198
Daugman, John      188
DCT      see "Discrete cosine transform"
de Moivre formula      101 119 214 215 235
De Moivre, Abraham      101
Decoupling      12—13
Delambre, Jean-Baptiste      11
Delprat, Nathalie      125
Delta function      see "Dirac $\delta$-function"
Denoising, Best Basis and Brahms recording      83—85
Denoising, defining noise      56
Denoising, new questions      85
Denoising, restoring singularities      52
Denoising, skeletons and      125
Denoising, wavelet maxima      59—61
Denoising, wavelet thresholding, Donoho and Johnstone      56-59
Denoising, wavelet thresholding, other      59—61
DeVore, Ronald      59
Differential equations      7—8 11—15 22 46 73 107
Digital technology      18—20
Dilation      41
Dimensionality reduction      189
Dirac $\delta$-function (delta function)      168 230 233
Dirac basis      168
Dirichlet, Gustave Lejeune      8 106 230
Discrete cosine transform      161
Discrete transforms      74—75 80 125 126 136
Distributions      107 182 184 229—230
Divergence      105 107
Donoho, David      56—59 61 85 89
Donovan, George      163
Dot product      see "Scalar product"
Dyadic      125
Dynamical systems      46 113
e (number)      101—102
Edison, Thomas      83
Egypt (and Fourier)      6
Einstein, Albert (speaking of Newton)      7
El Nino ocean current      53
Energy (of error)      135
Energy (of signal)      29—30 57 191 192 196
entropy      81 82
Epperson, Jay      70
Escudie, Bernard      124
Esteban, D. (and quadrature mirror filters)      147 162
Euler, Leonhard (and zeta function)      183
Event      172
Expectation      172
Exponential      102
Extended Self Similarity      56
Faraday, Michael (on mathematical writing)      xiii
Farge, Marie, choice of transform      76 200
Farge, Marie, choice of wavelet      74—75 194
Farge, Marie, interpreting coefficients      62 74
Farge, Marie, multiresolution analysis, importance of      39
Farge, Marie, wavelets and turbulence      71—72 78 189
Fast Fourier transform (FFT)      117—123
Fast Fourier transform (FFT), abuse of      21
Fast Fourier transform (FFT), alternative description      118
Fast Fourier transform (FFT), comparison with fast wavelet transform      161
Fast Fourier transform (FFT), discrete form of Fourier transform      118
Fast Fourier transform (FFT), history of      117 121
Fast Fourier transform (FFT), importance of      20 40 45 117
Fast Fourier transform (FFT), matrix form      119—123
Fast wavelet transform (FWT)      42—45 86 154—161
Fast wavelet transform (FWT), comparison with fast Fourier transform      161
Fast wavelet transform (FWT), concise      156
Fast wavelet transform (FWT), example with Haar scaling function and wavelet      156—157 159—161
Fast wavelet transform (FWT), importance of      40 45 139
Fast wavelet transform (FWT), scaling function in      42—44 154
Fast wavelet transform (FWT), speed of      45 139 155 161
Father function      41 see
FBI (Federal Bureau of Investigations)      83
Field, David J.      25 62 64 187—192
Filter coefficients      159
Filters      39 138 152 161
Filters, digital, frequencies of      147 151 230
Filters, high-pass filter      139 150 159
Filters, low-pass filter      138—139 147 159
Filters, shiftable filters      193
Filters, steerable filters      193
fingerprints      83
Fourier analysis      see also "Fourier series" "Fourier "Fourier
Fourier analysis, quantum mechanics and      15 17 51
Fourier analysis, significance of      7—8 11—19 51
Fourier analysis, solving differential equations      12—15
Fourier analysis, time information hidden      22—23 53
Fourier analysis, unsuited to nonlinear problems      73—74
Fourier coefficients      9 12—13 17—18 97—100 104 114—116 185
Fourier series of function that decreases at infinity      231
Fourier series, convergence of      104—113
Fourier series, formulas for      97—98
Fourier series, formulas for, using complex exponentials      102
Fourier transform      9 15 29 82 96—103 192 200 see "Fourier "Windowed "Fourier
Fourier transform of periodic function      227—230
Fourier transform of sequence of numbers      147 227—230
Fourier transform, "hat" notation      96 103
Fourier transform, amplitude      99
Fourier transform, computing      118—119
Fourier transform, formulas for:      101
Fourier transform, formulas for:, using complex exponentials      102 220
Fourier transform, phase      99—100
Fourier transform, physical reality of      15 62
Fourier, Joseph      5—9 11 14—15 17 117 181
Fractal wavelets      163—164
Fractals      11 54—56 59
frames      196
Frazier, Michael      3 20 70 219
Freeman, William T.      193
Frequency of digital filter      151
Frequency of wavelets, not precise      31 198—199
Frequency, doubles, with octaves      19
Frequency, measured: in hertz      96
Frequency, measured: in radians      212—213
Frequency, spatial      16 96—97
Frequency, variables representing      97—98 118
Frisch, Uriel      54—56
Function spaces      127 129 181—182 184—185 see
Function spaces, access to: with Fourier analysis      185—186
Function spaces, access to: with wavelets      26 186
Functions      9—10
Functions as point or vector in infinite-dimensional space      103 127—129 183—185
Functions, analyzing functions      15 126
Functions, history (changing definition)      10—11 181—186
Functions, length of      129 133
Functions, notation: f or f(x)      102—103
Functions, zeta function      183—184
FWT      see "Fast wavelet transform"
Gabor transforms      26—28 187 188
Gabor, Dennis, holography      22
Gabor, Dennis, importance of uncertainty principle in acoustics      49
Gabor, Dennis, limit of information transmissible      64
Gabor, Dennis, reservations about Fourier analysis      22—23
Gabor, Dennis, windowed Fourier analysis      23—24 26 31 187 203
Galand, C. (and quadrature mirror filters)      147 162
Gauss, Carl Friedrich (and fast Fourier transform)      20 117 121—122
Gelfand, Israel      107 182 184
Geronimo, Jeffrey S.      163—164
Gibbs' phenomenon      106
Gonnet, Caroline      125
Granlund, Goesta      187
Grasseau, G.      54
Gravitational waves, detection of      125
Grossmann, Alex, continuous wavelet transform      35
Grossmann, Alex, Daubechies      47
Grossmann, Alex, definition of wavelet a scholastic question      80
Grossmann, Alex, denoising      57
Grossmann, Alex, early involvement with wavelets      24—25 29—30 34 71
Grossmann, Alex, hearing and wavelets      62
Grossmann, Alex, influence of wavelets on interdisciplinary work      25
Grossmann, Alex, matrix compression      71
Grossmann, Alex, speed of computations      45
Guillemain, Philippe      125
H      see "Planck's constant"
h bar $(\hbar)$      179
Haar function      see "Haar wavelet"
Haar scaling function      141—143 145 148 149 156—157 159—161
Haar wavelet      36 141 152 156—157 159—161 163 196
Hardin, Douglas P.      163
Hausdorff, Felix      182
Healy, Dennis Jr.      53 70 78
Hearing      62—63
Heat diffusion      7—8 11—15 17
Heaviside, Oliver (and distributions)      184
Heisenberg boxes      168 205—207
Heisenberg cells      see "Heisenberg boxes"
Heisenberg uncertainty principle in communication theory and signal processing      48—51 165—170 171 199
Heisenberg uncertainty principle in quantum mechanics      49 51 171 176 178 180
Heisenberg uncertainty principle, proof      136 224—226
Hermite, Charles      181
Hertz      18 96
High-pass filter      see "Filters"
Hugo, Victor (on Fourier)      7
Hwang, Wen Liang (and wavelet maxima)      59 125
Hybrids      see "Malvar wavelets" "Wavelet
Image processing      38 68—70 78 125 137 138 139 140 162
Infinite product      149
Information, Kolmogorov information content      65 67
Information, not to be confused with meaning      67
Information, quantifying      64—65
Inner product      126 see
Innocent, Jean-Michel      125
Integrals      see also "Lebesgue integral" "Riemann
Integrals, comparison of Lebesgue and Riemann integrals      216—219
Integrals, computing coefficients with      30—33 98 114—116 131—133
Integrals, measuring continuous probability spaces      173—174
Integrals, relationship with scalar products      131—133
Integrals, zero, of wavelet      32 36
Integration      118
Isometry      225
Iterated Function Systems      146
iterations      46—47 86
Jacobi, Carl (on Fourier)      11
Jaffard, Stephane      55 186
Johnstone, Iain      56 59 61
Kam theorem      113
Kerkyacharian, Gerard      57
Koerner, T.W.      8 11 20 21
Kolmogorov, Andrei, compressibility of information      65—68
Kolmogorov, Andrei, definition of random      65
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