| Introduction | p. 1 |
| Some Words About the History of Computed Tomography | p. 7 |
| References | p. 19 |
| Technical Concepts of X-ray Computed Tomography Scanners | p. 21 |
| Data Acquisition Systems | p. 22 |
| First-Generation Scanners | p. 24 |
| Second-Generation Scanners | p. 25 |
| Third-Generation Scanners | p. 25 |
| Fourth-Generation Scanners | p. 27 |
| Spiral Scanners | p. 31 |
| X-ray Sources | p. 32 |
| The Physics of X-ray Sources | p. 33 |
| X-ray Tubes | p. 37 |
| Electrical Aspects of X-ray Tubes | p. 43 |
| X-ray Detectors | p. 45 |
| Detector Matrices | p. 48 |
| Detector Parameters | p. 48 |
| Imaging in Computed Tomography Devices | p. 52 |
| Luminance of the Image | p. 52 |
| Discretisation and Quantisation of the Image | p. 53 |
| The Display of Reconstructed Images | p. 56 |
| References | p. 60 |
| The Physics of Data Acquisition | p. 63 |
| X-ray Propagation Through Matters | p. 63 |
| The Radon Transform | p. 68 |
| X-ray Collimators | p. 72 |
| Physical Causes of Artefacts in the Reconstructed Image | p. 73 |
| Spectral Nonlinearities | p. 74 |
| Beam-width Nonlinearities | p. 77 |
| Scatter Nonlinearities | p. 78 |
| Metal Artefacts | p. 79 |
| Measurement Noise | p. 80 |
| References | p. 81 |
| Reconstruction from Parallel-beam Projections | p. 83 |
| Geometry of the Parallel-beam Scanner | p. 83 |
| Geometry of the Discrete Parallel-beam Scanner | p. 86 |
| Image Reconstruction from Projections: Problem Formulation | p. 93 |
| Reconstruction Methods by Convolution/Filtration and Back-Projection | p. 97 |
| Choice of the Filter Forms | p. 101 |
| Reconstruction Method by Convolution and Back-Projection | p. 110 |
| Discrete Implementation of the Reconstruction Method by Convolution and Back-Projection | p. 113 |
| Reconstruction Method by Filtration and Back-Projection | p. 117 |
| Discrete Implementation of the Reconstruction Method by Filtration and Back-Projection | p. 121 |
| References | p. 125 |
| Reconstruction from Fan-beam Projections | p. 127 |
| Geometry of the Fan-beam Scanner | p. 127 |
| Geometry of the Discrete Projection System | p. 129 |
| Reconstruction Method with Rebinning | p. 131 |
| Discrete Implementation of the Reconstruction Method with Rebinning | p. 133 |
| Direct Fan-beam Reconstruction Method | p. 135 |
| Discrete Implementation of the Direct Fan-beam Reconstruction Method | p. 141 |
| References | p. 147 |
| Spiral Tomography | p. 149 |
| Single Slice Computed Tomography-SSCT | p. 150 |
| The Geometry of the Scanner | p. 151 |
| The Geometry of the Discrete Scanner | p. 153 |
| The 360° LI Reconstruction Algorithm | p. 155 |
| Discrete Implementation of the 360° LI Reconstruction Method | p. 158 |
| The 180° LI Reconstruction Algorithm | p. 160 |
| Discrete Implementation of the 180° LI Reconstruction Method | p. 166 |
| Multi-Slice Computed Tomography-MSCT | p. 170 |
| The Geometry of the Scanner | p. 170 |
| The Geometry of the Discrete Scanner | p. 173 |
| The z-Filtering Reconstruction Algorithm | p. 176 |
| Discrete Implementation of the z-filtering Reconstruction Method | p. 181 |
| Cone-Beam Spiral Computed Tomography-CBCT | p. 185 |
| The Geometry of the Cone-Beam Scanner | p. 187 |
| The Geometry of the Discrete Cone-Beam Scanner | p. 190 |
| The Feldkamp Algorithm | p. 192 |
| Discrete Implementation of the Feldkamp Algorithm | p. 197 |
| The Advanced Single-Slice Rebinning Algorithm-ASSR | p. 201 |
| Discrete Implementation of the ASSR Algorithm | p. 224 |
| References | p. 228 |
| Algebraic Reconstruction Techniques | p. 233 |
| Formulation of the Algebraic Problem of Image Reconstruction from Projections | p. 234 |
| Algebraic Reconstruction Algorithms | p. 237 |
| Basic ART Algorithm | p. 237 |
| Practical Approach to the Basic ART Algorithm | p. 242 |
| ART Algorithm with Relaxation | p. 244 |
| Practical Approach to the ART Algorithm with Relaxation | p. 244 |
| Chaotic ART Algorithm | p. 245 |
| Practical Approach to the Chaotic ART Algorithm | p. 247 |
| Iterative Coordinate Descent Algorithm | p. 248 |
| The Geometry of the Projection System in 3D Space | p. 248 |
| Formulation of the Reconstruction Problem in Terms of Probability | p. 253 |
| Solving the Problem of Optimisation | p. 260 |
| Practical Approach to the Iterative Coordinate Descent Algorithm | p. 262 |
| References | p. 264 |
| Evaluation of CT Devices | p. 267 |
| Technical Parameters of CT Devices | p. 267 |
| Phantoms | p. 270 |
| ATS Phantom | p. 271 |
| Moström's Phantom | p. 271 |
| Low-contrast Resolution Phantom | p. 271 |
| Spatial Resolution Phantom | p. 272 |
| CT Linearity Phantom | p. 273 |
| Slice Thickness Phantom | p. 274 |
| Phantom Simulating a Skull Bone | p. 275 |
| Phantom Sets | p. 276 |
| Start-up and Test Procedures | p. 277 |
| References | p. 278 |
| Computer-Generated Projections for Simulations | p. 281 |
| Mathematical Model for Parallel-beam Projections | p. 282 |
| Mathematical Model for Fan-beam Projections | p. 287 |
| Mathematical Model for Cone-beam Spiral Projections | p. 288 |
| Introduction of Noise to the Projections | p. 294 |
| References | p. 295 |
| Functions and their Properties | p. 297 |
| Sample Code for Selected Functions | p. 307 |
| Index | p. 313 |
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