Computed radiation imaging: physics and mathematics of forward and inverse problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2011
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Elsevier insights
|
| Online-Zugang: | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=4243211&custom%5Fatt%5F2=simple%5Fviewer Inhaltsverzeichnis |
| Beschreibung: | XII, 290 S. graph. Darst. |
| ISBN: | 9780123877772 |
Internformat
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| 020 | |a 9780123877772 |9 978-0-12-387777-2 | ||
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| 100 | 1 | |a Hussein, Esam Mahmud Abu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computed radiation imaging |b physics and mathematics of forward and inverse problems |c Esam M. A. Hussein |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2011 | |
| 300 | |a XII, 290 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Elsevier insights | |
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Datensatz im Suchindex
| _version_ | 1804148670519574528 |
|---|---|
| adam_text | Titel: Computed radiation imaging
Autor: Hussein, Esam Mahmud Abu
Jahr: 2011
Contents
Preface xi
1 Radiation Imaging 1
1.1 Why Radiation? 1
1.2 Imaging Modalities 2
1.3 Direct and Reconstructed Imaging 6
1.4 The Forward and Inverse Problems 7
1.5 Forward and Inverse Mapping 10
Part I The Forward Problem 13
15
15
15
17
20
21
23
24
25
27
27
27
28
29
30
30
31
32
33
34
35
35
35
Radiation Transport
2.1 Introduction
2.2 Variables
2.3 Cross Sections
2.4 Boltzmann Transport Equation
2.5 Source-Free Steady-State Problem
2.6 Steady-State Problem in Void
2.7 Point-Kernel Method
2.8 Charged Particles
Measurement Models
3.1 Formulation
3.2 Scaling
3.3 Measured Response
3.4 Sensitivity
3.5 Variability
3.6 Components
3.6.1 Source
3.6.2 Detector
3.7 Image Grid
3.8 Idealization
3.9 Computer Coding
3.9.1 Verification
3.9.2 Validation
Contents
37
37
40
40
42
42
43
43
45
47
48
49
50
51
53
53
55
58
59
59
61
63
63
64
65
66
68
70
71
Part II The Inverse Problem 73
75
75
77
78
78
79
79
80
82
82
85
4 Transmission
4.1 Basic Model
4.2 Physical Relevance
4.2.1 Photons
4.2.2 Neutrons
4.3 Discretization
4.4 Nature of Radiation Source
4.4.1 Gamma Rays
4.4.2 X-Rays
4.4.3 Neutrons
4.5 Secondary Radiation
4.6 Scattering
4.7 Sensitivity
4.8 Variability
5 Emission
5.1 Embedded Radiation
5.2 Induced Emission
5.3 Discretization
5.4 Sensitivity
5.5 Sources
5.6 Interfering Effects
6 Scattering
6.1 Introduction
6.2 Single-Scattering Model
6.3 Multiple Scattering
6.4 Compton Scattering
6.5 Neutron Elastic Scattering
6.6 Discretization
6.7 Sensitivity
Features
7.1 Discretization
7.2 Well-Posed Problem
7.3 Existence
7.4 Uniqueness
7.5 Continuity
7.6 Ill-Posed Problem
7.7 Ill-Conditioning
7.A Basics of Functional Analysis
7.A.1 Within a Space
7.A.2 Mapping between Spaces
Contents vü
8 Formulation 87
8.1 Matrix 87
8.2 Functional 88
8.3 Analytic 89
8.3.1 Fourier Transform 89
8.3.2 Backprojection 91
8.4 Probabilistic 92
8.A Probabilistic Basis of Maximum-Likelihood and
Least-Squares Methods 94
9 Preprocessing of Measurements 97
9.1 Number of Measurements 98
9.1.1 Sampling 98
9.1.2 Error Minimization 100
9.2 Frequency Analysis 104
9.2.1 Frequency Filtering 105
9.2.2 Impulse Response 107
9.2.3 Detector Aperture 108
9.3 Spatial Filtering of Noise 109
9.3.1 Moving-Average Filter 109
9.3.2 Gaussian Filter 110
9.3.3 Recursive Weighted Moving Average Filter 111
9.3.4 Matched Filter 112
9.3.5 Multipole Filters 113
9.4 Consistency and Smoothing 113
9.4.1 Regularized Least-Squares 114
9.4.2 Dynamic Programming 115
9.4.3 Spline Smoothing 119
9.4.4 Cross Validation 120
9.4.5 Mollification 120
10 Matrix-Based Methods 125
10.1 Error Propagation 125
10.2 Singular Value Decomposition 126
10.3 Least Squares 128
10.4 Regularization Methods 128
10.4.1 Approach 128
10.4.2 Mathematical Significance 130
10.4.3 An Optimization Perspective 132
10.4.4 Minimum Information 133
10.4.5 Doubly Relaxed 134
10.4.6 Estimate of Solution 134
10.4.7 Gradient of Solution 134
10.4.8 Covariance Matrix 136
10.4.9 Spatial Correlation 137
Contents
10.4.10 Modeling-Error Compensation 138
10.4.11 Piecewise 139
10.4.12 Variational 146
10.4.13 Maximum Entropy 147
10.4.14 Solution Bounding 149
10.5 Regularization-Parameter Determination 150
10.5.1 Convergence Regularization 151
10.5.2 Discrepancy Principle 152
10.5.3 L-Curve 152
10.5.4 Minimum Predictive Error 153
10.5.5 Generalized Cross Validation 154
10.5.6 Minimum Bound 155
10.5.7 Statistical Hypothesis Testing 155
10.5.8 Regularization by Iteration 157
10.6 Iterative Methods 157
10.6.1 Geometric Approach 158
10.6.2 Successive Approximation 159
10.6.3 Steepest Descent 161
10.6.4 Conjugate Gradient 162
10.6.5 Convergence Metrics and Stopping Criteria 163
10.7 Nonlinear Problems 165
10.7.1 Quasi-Linearization 166
10.7.2 Successive Approximation 166
10.7.3 Newton-Raphson 167
10.7.4 Gauss-Newton 168
10.7.5 Levenberg-Marquardt 168
10.7.6 Conjugate Gradient 169
10.8 Software 169
11 Functional Optimization 173
11.1 Formulation 173
11.2 Effect of Number of Measurements 175
11.3 Sensitivity to Measurement Uncertainty 176
11.4 Minimization 177
11.5 Search Methods 177
11.5.1 Sequential Linearization 177
11.5.2 Gradient Driven 178
11.6 Genetic Evolution 178
11.7 Simulated Annealing 180
11.8 Neural Networks 182
12 Analytic Methods 185
12.1 Radon Transform 185
12.2 Two-Dimensional Fourier Transforms 187
12.2.1 Fundamental Equations 187
Contents
12.2.2 Completeness and Continuity 190
12.2.3 Discretization 190
12.2.4 Interpolation 193
12.2.5 Direct Fourier Inversion 194
12.2.6 Fourier-Frequency Filtering 195
12.3 Backprojection 195
12.3.1 Direct 196
12.3.2 Fourier Filtered 197
12.3.3 Radon Filtered 198
12.3.4 Shepp-Logan Filtered 198
12.3.5 Convolution Filtered 199
12.3.6 Noise Filtering 201
12.3.7 Error Propagation 201
12.4 Fan-Beam Transmission Tomography 202
12.4.1 Rebinning 202
12.4.2 Direct Backprojection 204
12.5 Cone-Beam Transmission Tomography 206
12.6 Emission Imaging 208
12.7 Scatter Imaging 213
12.8 Computer Codes 214
12.9 Wavelet Transforms 214
13 Probabilistic Methods 219
13.1 Bayesian - Minimum Information 219
13.2 Poisson Distribution 221
13.3 Normal Distribution 223
13.4 Maximum a posteriori (map) 224
13.5 The Monte Carlo Method 228
14 Incomplete Problems 231
14.1 Incompleteness 231
14.2 General Solution Methods 232
14.2.1 Least-Squares Solution 232
14.2.2 Twomey-Phillips Solution 232
14.2.3 Algebraic Geometric Solution 233
14.2.4 Pseudoinversion 233
14.2.5 Optimization Methods 233
14.2.6 Analytic Solutions 233
14.2.7 Probabilistic Solution 234
14.3 Estimation Maximization 234
14.3.1 Poisson Distribution Likelihood 236
14.3.2 Scatter Imaging 240
14.3.3 Ordered Subset Estimation Maximization 241
14.4 Markov Random Fields 241
Contents
15 Testing 245
245
247
250
251
251
252
253
253
255
256
257
262
264
265
266
266
267
268
16 Post-Processing: Image Enhancement 271
272
274
274
276
277
277
278
278
279
279
280
280
281
282
283
284
Bibliography 289
Testing
15.1 Ideal Problem
15.2 Noisy-Ideal Problem
15.3 Independently-Simulated-Data Problem
15.4 Laboratory Problem
15.4.1 Background
15.4.2 Inaccuracy
15.4.3 Measurement Uncertainties
15.4.4 Calibration
15.4.5 Inexactness
15.5 Image Quality
15.5.1 Spatial Resolution
15.5.2 Contrast
15.5.3 Sensitivity
15.5.4 Accuracy and Precision
15.5.5 Systematic Artifacts
15.6 Test Objects
15.6.1 Single Inserts
15.6.2 Multiple Inserts
Post-Processing: Image Enhancement
16.1 Image Convolution
16.2 Image Degradation
16.2.1 Point Spread Function
16.2.2 Noise
16.3 Frequency Filtering
16.3.1 Gaussian Filter
16.3.2 Parzen Filter
16.3.3 Pseudoinverse/Matched Filter
16.3.4 Wiener Filter
16.3.5 Power Spectrum Equalization Filter
16.3.6 Metz Filter
16.3.7 Frequency-Dependent Filters
16.4 Matrix Based
16.5 Statistical Methods
16.6 Optimization
16.7 Blind Deconvolution
|
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| author | Hussein, Esam Mahmud Abu |
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| author_variant | e m a h ema emah |
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| discipline | Physik Medizin |
| edition | 1. ed. |
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| spelling | Hussein, Esam Mahmud Abu Verfasser aut Computed radiation imaging physics and mathematics of forward and inverse problems Esam M. A. Hussein 1. ed. Amsterdam [u.a.] Elsevier 2011 XII, 290 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elsevier insights http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=4243211&custom%5Fatt%5F2=simple%5Fviewer HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024620352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hussein, Esam Mahmud Abu Computed radiation imaging physics and mathematics of forward and inverse problems |
| title | Computed radiation imaging physics and mathematics of forward and inverse problems |
| title_auth | Computed radiation imaging physics and mathematics of forward and inverse problems |
| title_exact_search | Computed radiation imaging physics and mathematics of forward and inverse problems |
| title_full | Computed radiation imaging physics and mathematics of forward and inverse problems Esam M. A. Hussein |
| title_fullStr | Computed radiation imaging physics and mathematics of forward and inverse problems Esam M. A. Hussein |
| title_full_unstemmed | Computed radiation imaging physics and mathematics of forward and inverse problems Esam M. A. Hussein |
| title_short | Computed radiation imaging |
| title_sort | computed radiation imaging physics and mathematics of forward and inverse problems |
| title_sub | physics and mathematics of forward and inverse problems |
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