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Natterer F. — The Mathematics of Computerized Tomography (Classics in Applied Mathematics)
Natterer F. — The Mathematics of Computerized Tomography (Classics in Applied Mathematics)

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Название: The Mathematics of Computerized Tomography (Classics in Applied Mathematics)

Автор: Natterer F.

Аннотация:

This book provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms. It focuses on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science, and engineering. The Mathematics of Computerized Tomography covers the relevant mathematical theory of the Radon transform and related transforms and also studies more practical questions such as stability, sampling, resolution, and accuracy. Quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithms, for both standard problems and problems with incomplete data.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 222

Добавлена в каталог: 27.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
a priori information      90 94 95
Abel type integral equation      23 24 26
Adjoint      18 140
Algebraic reconstruction technique (ART)      102 137 138 140 144 160 164 170
Aliasing      60 113
Approximate delta-function      183
Artefacts      118 120 121 159 164 168
Attenuated radon transform      46 52 53
B-spline      60 107 120 121
Backprojection      103 113 148 151 153
Band-limited      54
Bandwidth      54
Beam hardening      3
Bessel functions      197
Cauchy principal value      185
Chebyshev polynomials      154
Chirp z-algorithm      127 212
Collocation method      137
Communication theory      54 184
Completion of data      159 162 166 168 170 178
Conditional expectation      91
Cone beam scanning      3 147 174
Consistency conditions      37 49 159 168
Cormack’s inversion formula      28 155 166
Covariance      91
Cut-off frequency      60
Debye’s formula      198
Diffraction tomography      5
Digital filtering      89
Dirac’s delta-function      183
Direct Algebraic method      102 146 149 160 168
Discrete Fourier Transform      206
Displacement rank      208
Distributions      181
Divergent beam transform      10 33
Dual operators      13 47
Electron microscopy      3
Emission CT      4 47
Essentially band-limited      55
Exponential radon transform      47
Exterior problem      28 30 101 146 158 166 168
Fan-beam geometry      82
Fan-beam scanning      2 10 75 83 111
Fast Fourier transform (FFT)      11 119 120 125 126 148 164 206 207
Filtered backprojection      49 102 103 106 113 117 128 151 159 164 168
Filtered layergram      22 48 153
Filtering      60
Fourier coefficients      182
Fourier expansion      184
Fourier inversion formula      180
Fourier reconstruction      102 119 120 156
Fourier transform      180
Funk — Hecke theorem      195
Gamma function      193
Gauss — Legendre formula      191
Gegenbauer polynomials      193
Generalized inverse      85
Haar measure      189
Hilbert transform      186
Hole theorem      30
Ideal low-pass      60
Ill-posed      33 42 85 95 158 164 166 168
Incomplete data      2 85 147 158
Indeterminacy      36 90
Integral geometry      5 14
Interior problem      146 158 169
Interlaced parallel geometry      71 74 83
Interpolation of functions      107 108 120 125 126 127
Interpolation of spaces      46 60 201 202 203
Inversion formulas      18 48 49 100 102 119 153 171
Isotropic exponential model      92
Jacobi polynomials      100
k-plane transform      52
Kaczmarz method      102 128 134 136 137 139
Legendre functions      197
Legendre polynomials      194
Limited angle problem      3 158 160 163 164 166
Locality      21 172
m-resolving      64
Mellin transform      194
Mildly ill-posed      91
Minimal norm solution      170
Modestly ill-posed      91
NMR imaging      8
Normal equations      86
Nyquist condition      56
Optimality relation      83 118 120 127
Oversampling      56
Parallel scanning      2 71 111 117
Parseval’s relation      183
PET (Positron Emission Tomography)      4 76 82 83 153
Picture densities      94
pixels      137
Plancherel’s theorem      182
Poisson’s formula      184
Projection theorem      47 119
Pseudo-differential operators      172
Quadrature rule      103 106 190
Radar      8
Radon transform      9
Radon’s inversion formula      22 151 158 169
Random variables      91
Rebinning      111
Regularization      86 178
Relaxation parameter      128
Resolution      64 68 71 106 111 115 116
Restricted source problem      158
Riesz potential      18
Rotational invariance      146 147 148
Rytov approximation      6
Sampling      54 71 75 180
Scanning geometries      2 71 83 108
Schwartz space      9
Semi-convergence      89 144
Severely ill-posed      91 160 163 166
Shah-distribution      184
Sine function      55
Sine series      57
Singular value decomposition      85 86 88 95 100 101 160 161
Sobolev spaces      42 92 94 95 121 200
SOR      136
Spectral radius      135
Spherical coordinates      186
Spherical harmonic      195
Stability estimate      160 174
Three-dimensional CT      3 32 174
Tikhonov — Phillips method      89 91 148 164
Toeplitz matrix      146 148 161 164 206 208 209
Tomography      8
Transmission CT      1
Trapezoidal rule      56 109 184 191
Tuy’s condition      174
Ultrasound CT      4
Undersampling      57 118
Weber — Schafheitlin integral      199
White noise      91
Worst case error      90
X-ray transform      9
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