1 Introduction ................................................. 1
2 Some Words About the History of Computed Tomography .......... 7
References .................................................. 19
3 Technical Concepts of X-ray Computed Tomography Scanners .... 21
3.1 Data Acquisition Systems ............................... 22
3.2 X-ray Sources .......................................... 32
3.3 X-ray Detectors ........................................ 45
3.4 Imaging in Computed Tomography Devices ................. 52
References .................................................. 60
4 The Physics of Data Acquisition ............................. 63
4.1 X-ray Propagation Through Matters ...................... 63
4.2 The Radon Transform .................................... 68
4.3 X-ray Collimators ...................................... 72
4.4 Physical Causes of Artefacts in the Reconstructed
Image .................................................. 73
References .................................................. 81
5 Reconstruction from Parallel-beam Projections ............... 83
5.1 Geometry of the Parallel-beam Scanner .................. 83
5.2 Geometry of the Discrete Parallel-beam Scanner ......... 86
5.3 Image Reconstruction from Projections: Problem
Formulation ............................................ 93
5.4 Reconstruction Methods by Convolution/Filtration
and Back-Projection .................................... 97
References ................................................. 125
6 Reconstruction from Fan-beam Projections ................... 127
6.1 Geometry of the Fan-beam Scanner ...................... 127
6.2 Geometry of the Discrete Projection System ............ 129
6.3 Reconstruction Method with Rebinning .................. 131
6.4 Discrete Implementation of the Reconstruction Method
with Rebinning ........................................ 133
6.5 Direct Fan-beam Reconstruction Method ................. 135
6.6 Discrete Implementation of the Direct Fan-beam
Reconstruction Method ................................. 141
References ................................................. 147
7 Spiral Tomography .......................................... 149
7.1 Single Slice Computed Tomography - SSCT ............... 150
7.2 Multi-Slice Computed Tomography - MSCT ................ 170
7.3 Cone-Beam Spiral Computed Tomography - CBCT ........... 185
References ................................................. 228
8 Algebraic Reconstruction Techniques ........................ 233
8.1 Formulation of the Algebraic Problem of Image
Reconstruction from Projections ....................... 234
8.2 Algebraic Reconstruction Algorithms ................... 237
8.3 Iterative Coordinate Descent Algorithm ................ 248
8.4 Practical Approach to the Iterative Coordinate
Descent Algorithm ..................................... 262
References ................................................. 264
9 Evaluation of CT Devices ................................... 267
9.1 Technical Parameters of CT Devices .................... 267
9.2 Phantoms .............................................. 270
9.3 Start-up and Test Procedures .......................... 277
References ................................................. 278
10 Computer-Generated Projections for Simulations ............. 281
10.1 Mathematical Model for Parallel-beam Projections ...... 282
10.2 Mathematical Model for Fan-beam Projections ........... 287
10.3 Mathematical Model for Cone-beam Spiral Projections ... 288
10.4 Introduction of Noise to the Projections .............. 294
References ................................................. 295
Appendix A: Functions and their Properties .................... 297
Appendix B: Sample Code for Selected Functions ................ 307
Index ......................................................... 313
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