Tomography

The principle of tomography is to explore the structure and composition of objects non-destructively along spatial and temporal dimensions, using penetrating radiation, such as X- and gamma-rays, or waves, such as electromagnetic and acoustic waves. Based on computer-assisted image reconstruction, tomography provides maps of parameters that characterize the emission of the employed radiation or waves, or their interaction with the examined objects, for one or several cross-sections. Thus, it gives access to the inner structure of inert objects and living organisms in their full complexity. In this book, multidisciplinary specialists explain the foundations and principles of tomographic imaging and describe a broad range of applications. The content is organized in five parts, which are dedicated to image reconstruction, microtomography, industrial tomography, morphological medical tomography and functional medical tomography.

Preface xvii

Notation xxi

Chapter 1. Introduction to Tomography 1
Pierre GRANGEAT

1.1. Introduction 1

1.2. Observing contrasts 2

1.3. Localization in space and time 7

1.4. Image reconstruction 9

1.5. Application domains 12

1.6. Bibliography 17

PART 1. IMAGE RECONSTRUCTION 21

Chapter 2. Analytical Methods 23
Michel DEFRISE and Pierre GRANGEAT

2.1. Introduction 23

2.2. 2D Radon transform in parallel-beam geometry 25

2.3. 2D Radon transform in fan-beam geometry 32

2.4. 3D X-ray transform in parallel-beam geometry 37

2.5. 3D Radon transform 40

2.6. 3D positron emission tomography 42

2.7. X-ray tomography in cone-beam geometry 46

2.8. Dynamic tomography 54

2.9. Bibliography . 58

Chapter 3. Sampling Conditions in Tomography 63
Laurent DESBAT and Catherine MENNESSIER

3.1. Sampling of functions in R6ᶰ 3

3.2. Sampling of the 2D Radon transform 71

3.3. Sampling in 3D tomography 79

3.4. Bibliography 85

Chapter 4. Discrete Methods 89
Habib BENALI and Françoise PEYRIN

4.1. Introduction 89

4.2. Discrete models 90

4.3. Algebraic methods 92

4.4. Statistical methods 99

4.5. Example of tomographic reconstruction 110

4.6. Discussion and conclusion 110

4.7. Bibliography 112

PART 2. MICROTOMOGRAPHY 117

Chapter 5. Tomographic Microscopy 119
Yves USSON and Catherine SOUCHIER

5.1. Introduction 119

5.2. Projection tomography in electron microscopy 120

5.3. Tomography by optical sectioning 121

5.4. 3D data processing, reconstruction and analysis 129

5.5. Bibliography 138

Chapter 6. Optical Tomography 141
Christian DEPEURSINGE

6.1. Introduction 141

6.2. Interaction of light with matter 142

6.3. Propagation of photons in diffuse media 150

6.4. Optical tomography methods 164

6.5. Optical tomography in highly diffuse media 181

6.6. Bibliography 190

Chapter 7. Synchrotron Tomography 197
Anne-Marie CHARVET and Françoise PEYRIN

7.1. Introduction 197

7.2. Synchrotron radiation 197

7.3. Quantitative tomography 202

7.4. Microtomography using synchrotron radiation 206

7.5. Extensions 210

7.6. Conclusion 211

7.7. Bibliography 212

PART 3. INDUSTRIAL TOMOGRAPHY 215

Chapter 8. X-ray Tomography in Industrial Non-destructive Testing 217
Gilles PEIX, Philippe DUVAUCHELLE and Jean-Michel LETANG

8.1. Introduction 217

8.2. Physics of the measurement 218

8.3. Sources of radiation 219

8.4. Detection 220

8.5. Reconstruction algorithms and artifacts 223

8.6. Applications 224

8.7. Conclusion 235

8.8. Bibliography 236

Chapter 9. Industrial Applications of Emission Tomography for Flow Visualization 239
Samuel LEGOUPIL and Ghislain PASCAL

9.1. Industrial applications of emission tomography 239

9.2. Examples of applications 242

9.3. Physical model of data acquisition 247

9.4. Definition and characterization of a system 252

9.5. Conclusion 255

9.6. Bibliography 255

PART 4.MORPHOLOGICAL MEDICAL TOMOGRAPHY 257

Chapter 10. Computed Tomography 259
Jean-Louis AMANS and Gilbert FERRETTI

10.1. Introduction 259

10.2. Physics of helical tomography 265

10.3. Applications of volume CT 272

10.4. Conclusion 279

10.5. Bibliography 280

Chapter 11. Interventional X-ray Volume Tomography 287
Michael GRASS, RégisGUILLEMAUD and Volker RASCHE

11.1. Introduction 287

11.2. Example of 3D angiography 290

11.3. Clinical examples 297

11.4. Conclusion 302

11.5. Bibliography 303

Chapter 12. Magnetic Resonance Imaging 307
André BRIGUET and Didier REVEL

12.1. Introduction 307

12.2. Nuclear paramagnetism and its measurement 308

12.3. Spatial encoding of the signal and image reconstruction 312

12.4. Contrast factors and examples of applications 318

12.5. Tomography or volumetry? 323

12.6. Bibliography 323

PART 5. FUNCTIONAL MEDICAL TOMOGRAPHY 327

Chapter 13. Single Photon Emission Computed Tomography 329
Irène BUVAT, Jacques DARCOURT and Philippe FRANKEN

13.1. Introduction 329

13.2. Radiopharmaceuticals 330

13.3. Detector 331

13.4. Image reconstruction 336

13.5. Example of myocardial SPECT 343

13.6. Conclusion 346

13.7. Bibliography 348

Chapter 14. Positron Emission Tomography 351
Michel DEFRISE and Régine TRÉBOSSEN

14.1. Introduction 351

14.2. Data acquisition 353

14.3. Data processing 363

14.4. Research and clinical applications of PET 370

14.5. Conclusion 373

14.6. Bibliography 374

Chapter 15. Functional Magnetic Resonance Imaging 377
Christoph SEGEBARTH andMichel DÉCORPS

15.1. Introduction 377

15.2. Functional MRI of cerebrovascular responses 378

15.3. fMRI of BOLD contrasts 380

15.4. Different protocols 383

15.5. Bibliography 389

Chapter 16. Tomography of Electrical Cerebral Activity in Magneto- and Electro-encephalography 393
Line Garnero

16.1. Introduction 393

16.2. Principles of MEG and EEG 394

16.3. Imaging of electrical activity of the brain based on MEG and EEG signals 398

16.4. Conclusion 407

16.5. Bibliography 408

List of Authors 411

Index 417

Pierre Grangeat (Telecommunication Engineer, Ph.D., IEEE Senior Member) is a Research Director at CEA, LETI, MINATEC, in Grenoble, France. His field of research covers information processing for biomedical technologies.