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.

• Preface xvii Notation xxiChapter 1. Introduction to Tomography 1Pierre GRANGEAT1.1. Introduction 11.2. Observing contrasts 21.3. Localization in space and time 71.4. Image reconstruction 91.5. Application domains 121.6. Bibliography 17PART 1. IMAGE RECONSTRUCTION 21Chapter 2. Analytical Methods 23Michel DEFRISE and Pierre GRANGEAT2.1. Introduction 232.2. 2D Radon transform in parallel-beam geometry 252.3. 2D Radon transform in fan-beam geometry 322.4. 3D X-ray transform in parallel-beam geometry 372.5. 3D Radon transform 402.6. 3D positron emission tomography 422.7. X-ray tomography in cone-beam geometry 462.8. Dynamic tomography 542.9. Bibliography . 58Chapter 3. Sampling Conditions in Tomography 63Laurent DESBAT and Catherine MENNESSIER3.1. Sampling of functions in R6ᶰ 33.2. Sampling of the 2D Radon transform 713.3. Sampling in 3D tomography 793.4. Bibliography 85Chapter 4. Discrete Methods 89Habib BENALI and Françoise PEYRIN4.1. Introduction 894.2. Discrete models 904.3. Algebraic methods 924.4. Statistical methods 994.5. Example of tomographic reconstruction 1104.6. Discussion and conclusion 1104.7. Bibliography 112PART 2. MICROTOMOGRAPHY 117Chapter 5. Tomographic Microscopy 119Yves USSON and Catherine SOUCHIER5.1. Introduction 1195.2. Projection tomography in electron microscopy 1205.3. Tomography by optical sectioning 1215.4. 3D data processing, reconstruction and analysis 1295.5. Bibliography 138Chapter 6. Optical Tomography 141Christian DEPEURSINGE6.1. Introduction 1416.2. Interaction of light with matter 1426.3. Propagation of photons in diffuse media 1506.4. Optical tomography methods 1646.5. Optical tomography in highly diffuse media 1816.6. Bibliography 190Chapter 7. Synchrotron Tomography 197Anne-Marie CHARVET and Françoise PEYRIN7.1. Introduction 1977.2. Synchrotron radiation 1977.3. Quantitative tomography 2027.4. Microtomography using synchrotron radiation 2067.5. Extensions 2107.6. Conclusion 2117.7. Bibliography 212PART 3. INDUSTRIAL TOMOGRAPHY 215Chapter 8. X-ray Tomography in Industrial Non-destructive Testing 217Gilles PEIX, Philippe DUVAUCHELLE and Jean-Michel LETANG8.1. Introduction 2178.2. Physics of the measurement 2188.3. Sources of radiation 2198.4. Detection 2208.5. Reconstruction algorithms and artifacts 2238.6. Applications 2248.7. Conclusion 2358.8. Bibliography 236Chapter 9. Industrial Applications of Emission Tomography for Flow Visualization 239Samuel LEGOUPIL and Ghislain PASCAL9.1. Industrial applications of emission tomography 2399.2. Examples of applications 2429.3. Physical model of data acquisition 2479.4. Definition and characterization of a system 2529.5. Conclusion 2559.6. Bibliography 255PART 4.MORPHOLOGICAL MEDICAL TOMOGRAPHY 257Chapter 10. Computed Tomography 259Jean-Louis AMANS and Gilbert FERRETTI10.1. Introduction 25910.2. Physics of helical tomography 26510.3. Applications of volume CT 27210.4. Conclusion 27910.5. Bibliography 280Chapter 11. Interventional X-ray Volume Tomography 287Michael GRASS, RégisGUILLEMAUD and Volker RASCHE11.1. Introduction 28711.2. Example of 3D angiography 29011.3. Clinical examples 29711.4. Conclusion 30211.5. Bibliography 303Chapter 12. Magnetic Resonance Imaging 307André BRIGUET and Didier REVEL12.1. Introduction 30712.2. Nuclear paramagnetism and its measurement 30812.3. Spatial encoding of the signal and image reconstruction 31212.4. Contrast factors and examples of applications 31812.5. Tomography or volumetry? 32312.6. Bibliography 323PART 5. FUNCTIONAL MEDICAL TOMOGRAPHY 327Chapter 13. Single Photon Emission Computed Tomography 329Irène BUVAT, Jacques DARCOURT and Philippe FRANKEN13.1. Introduction 32913.2. Radiopharmaceuticals 33013.3. Detector 33113.4. Image reconstruction 33613.5. Example of myocardial SPECT 34313.6. Conclusion 34613.7. Bibliography 348Chapter 14. Positron Emission Tomography 351Michel DEFRISE and Régine TRÉBOSSEN14.1. Introduction 35114.2. Data acquisition 35314.3. Data processing 36314.4. Research and clinical applications of PET 37014.5. Conclusion 37314.6. Bibliography 374Chapter 15. Functional Magnetic Resonance Imaging 377Christoph SEGEBARTH andMichel DÉCORPS15.1. Introduction 37715.2. Functional MRI of cerebrovascular responses 37815.3. fMRI of BOLD contrasts 38015.4. Different protocols 38315.5. Bibliography 389Chapter 16. Tomography of Electrical Cerebral Activity in Magneto- and Electro-encephalography 393Line Garnero16.1. Introduction 39316.2. Principles of MEG and EEG 39416.3. Imaging of electrical activity of the brain based on MEG and EEG signals 39816.4. Conclusion 40716.5. Bibliography 408List of Authors 411Index 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.

• Preface xvii Notation xxiChapter 1. Introduction to Tomography 1Pierre GRANGEAT1.1. Introduction 11.2. Observing contrasts 21.3. Localization in space and time 71.4. Image reconstruction 91.5. Application domains 121.6. Bibliography 17PART 1. IMAGE RECONSTRUCTION 21Chapter 2. Analytical Methods 23Michel DEFRISE and Pierre GRANGEAT2.1. Introduction 232.2. 2D Radon transform in parallel-beam geometry 252.3. 2D Radon transform in fan-beam geometry 322.4. 3D X-ray transform in parallel-beam geometry 372.5. 3D Radon transform 402.6. 3D positron emission tomography 422.7. X-ray tomography in cone-beam geometry 462.8. Dynamic tomography 542.9. Bibliography . 58Chapter 3. Sampling Conditions in Tomography 63Laurent DESBAT and Catherine MENNESSIER3.1. Sampling of functions in R6ᶰ 33.2. Sampling of the 2D Radon transform 713.3. Sampling in 3D tomography 793.4. Bibliography 85Chapter 4. Discrete Methods 89Habib BENALI and Françoise PEYRIN4.1. Introduction 894.2. Discrete models 904.3. Algebraic methods 924.4. Statistical methods 994.5. Example of tomographic reconstruction 1104.6. Discussion and conclusion 1104.7. Bibliography 112PART 2. MICROTOMOGRAPHY 117Chapter 5. Tomographic Microscopy 119Yves USSON and Catherine SOUCHIER5.1. Introduction 1195.2. Projection tomography in electron microscopy 1205.3. Tomography by optical sectioning 1215.4. 3D data processing, reconstruction and analysis 1295.5. Bibliography 138Chapter 6. Optical Tomography 141Christian DEPEURSINGE6.1. Introduction 1416.2. Interaction of light with matter 1426.3. Propagation of photons in diffuse media 1506.4. Optical tomography methods 1646.5. Optical tomography in highly diffuse media 1816.6. Bibliography 190Chapter 7. Synchrotron Tomography 197Anne-Marie CHARVET and Françoise PEYRIN7.1. Introduction 1977.2. Synchrotron radiation 1977.3. Quantitative tomography 2027.4. Microtomography using synchrotron radiation 2067.5. Extensions 2107.6. Conclusion 2117.7. Bibliography 212PART 3. INDUSTRIAL TOMOGRAPHY 215Chapter 8. X-ray Tomography in Industrial Non-destructive Testing 217Gilles PEIX, Philippe DUVAUCHELLE and Jean-Michel LETANG8.1. Introduction 2178.2. Physics of the measurement 2188.3. Sources of radiation 2198.4. Detection 2208.5. Reconstruction algorithms and artifacts 2238.6. Applications 2248.7. Conclusion 2358.8. Bibliography 236Chapter 9. Industrial Applications of Emission Tomography for Flow Visualization 239Samuel LEGOUPIL and Ghislain PASCAL9.1. Industrial applications of emission tomography 2399.2. Examples of applications 2429.3. Physical model of data acquisition 2479.4. Definition and characterization of a system 2529.5. Conclusion 2559.6. Bibliography 255PART 4.MORPHOLOGICAL MEDICAL TOMOGRAPHY 257Chapter 10. Computed Tomography 259Jean-Louis AMANS and Gilbert FERRETTI10.1. Introduction 25910.2. Physics of helical tomography 26510.3. Applications of volume CT 27210.4. Conclusion 27910.5. Bibliography 280Chapter 11. Interventional X-ray Volume Tomography 287Michael GRASS, RégisGUILLEMAUD and Volker RASCHE11.1. Introduction 28711.2. Example of 3D angiography 29011.3. Clinical examples 29711.4. Conclusion 30211.5. Bibliography 303Chapter 12. Magnetic Resonance Imaging 307André BRIGUET and Didier REVEL12.1. Introduction 30712.2. Nuclear paramagnetism and its measurement 30812.3. Spatial encoding of the signal and image reconstruction 31212.4. Contrast factors and examples of applications 31812.5. Tomography or volumetry? 32312.6. Bibliography 323PART 5. FUNCTIONAL MEDICAL TOMOGRAPHY 327Chapter 13. Single Photon Emission Computed Tomography 329Irène BUVAT, Jacques DARCOURT and Philippe FRANKEN13.1. Introduction 32913.2. Radiopharmaceuticals 33013.3. Detector 33113.4. Image reconstruction 33613.5. Example of myocardial SPECT 34313.6. Conclusion 34613.7. Bibliography 348Chapter 14. Positron Emission Tomography 351Michel DEFRISE and Régine TRÉBOSSEN14.1. Introduction 35114.2. Data acquisition 35314.3. Data processing 36314.4. Research and clinical applications of PET 37014.5. Conclusion 37314.6. Bibliography 374Chapter 15. Functional Magnetic Resonance Imaging 377Christoph SEGEBARTH andMichel DÉCORPS15.1. Introduction 37715.2. Functional MRI of cerebrovascular responses 37815.3. fMRI of BOLD contrasts 38015.4. Different protocols 38315.5. Bibliography 389Chapter 16. Tomography of Electrical Cerebral Activity in Magneto- and Electro-encephalography 393Line Garnero16.1. Introduction 39316.2. Principles of MEG and EEG 39416.3. Imaging of electrical activity of the brain based on MEG and EEG signals 39816.4. Conclusion 40716.5. Bibliography 408List of Authors 411Index 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.

• Preface xvii Notation xxiChapter 1. Introduction to Tomography 1Pierre GRANGEAT1.1. Introduction 11.2. Observing contrasts 21.3. Localization in space and time 71.4. Image reconstruction 91.5. Application domains 121.6. Bibliography 17PART 1. IMAGE RECONSTRUCTION 21Chapter 2. Analytical Methods 23Michel DEFRISE and Pierre GRANGEAT2.1. Introduction 232.2. 2D Radon transform in parallel-beam geometry 252.3. 2D Radon transform in fan-beam geometry 322.4. 3D X-ray transform in parallel-beam geometry 372.5. 3D Radon transform 402.6. 3D positron emission tomography 422.7. X-ray tomography in cone-beam geometry 462.8. Dynamic tomography 542.9. Bibliography . 58Chapter 3. Sampling Conditions in Tomography 63Laurent DESBAT and Catherine MENNESSIER3.1. Sampling of functions in R6ᶰ 33.2. Sampling of the 2D Radon transform 713.3. Sampling in 3D tomography 793.4. Bibliography 85Chapter 4. Discrete Methods 89Habib BENALI and Françoise PEYRIN4.1. Introduction 894.2. Discrete models 904.3. Algebraic methods 924.4. Statistical methods 994.5. Example of tomographic reconstruction 1104.6. Discussion and conclusion 1104.7. Bibliography 112PART 2. MICROTOMOGRAPHY 117Chapter 5. Tomographic Microscopy 119Yves USSON and Catherine SOUCHIER5.1. Introduction 1195.2. Projection tomography in electron microscopy 1205.3. Tomography by optical sectioning 1215.4. 3D data processing, reconstruction and analysis 1295.5. Bibliography 138Chapter 6. Optical Tomography 141Christian DEPEURSINGE6.1. Introduction 1416.2. Interaction of light with matter 1426.3. Propagation of photons in diffuse media 1506.4. Optical tomography methods 1646.5. Optical tomography in highly diffuse media 1816.6. Bibliography 190Chapter 7. Synchrotron Tomography 197Anne-Marie CHARVET and Françoise PEYRIN7.1. Introduction 1977.2. Synchrotron radiation 1977.3. Quantitative tomography 2027.4. Microtomography using synchrotron radiation 2067.5. Extensions 2107.6. Conclusion 2117.7. Bibliography 212PART 3. INDUSTRIAL TOMOGRAPHY 215Chapter 8. X-ray Tomography in Industrial Non-destructive Testing 217Gilles PEIX, Philippe DUVAUCHELLE and Jean-Michel LETANG8.1. Introduction 2178.2. Physics of the measurement 2188.3. Sources of radiation 2198.4. Detection 2208.5. Reconstruction algorithms and artifacts 2238.6. Applications 2248.7. Conclusion 2358.8. Bibliography 236Chapter 9. Industrial Applications of Emission Tomography for Flow Visualization 239Samuel LEGOUPIL and Ghislain PASCAL9.1. Industrial applications of emission tomography 2399.2. Examples of applications 2429.3. Physical model of data acquisition 2479.4. Definition and characterization of a system 2529.5. Conclusion 2559.6. Bibliography 255PART 4.MORPHOLOGICAL MEDICAL TOMOGRAPHY 257Chapter 10. Computed Tomography 259Jean-Louis AMANS and Gilbert FERRETTI10.1. Introduction 25910.2. Physics of helical tomography 26510.3. Applications of volume CT 27210.4. Conclusion 27910.5. Bibliography 280Chapter 11. Interventional X-ray Volume Tomography 287Michael GRASS, RégisGUILLEMAUD and Volker RASCHE11.1. Introduction 28711.2. Example of 3D angiography 29011.3. Clinical examples 29711.4. Conclusion 30211.5. Bibliography 303Chapter 12. Magnetic Resonance Imaging 307André BRIGUET and Didier REVEL12.1. Introduction 30712.2. Nuclear paramagnetism and its measurement 30812.3. Spatial encoding of the signal and image reconstruction 31212.4. Contrast factors and examples of applications 31812.5. Tomography or volumetry? 32312.6. Bibliography 323PART 5. FUNCTIONAL MEDICAL TOMOGRAPHY 327Chapter 13. Single Photon Emission Computed Tomography 329Irène BUVAT, Jacques DARCOURT and Philippe FRANKEN13.1. Introduction 32913.2. Radiopharmaceuticals 33013.3. Detector 33113.4. Image reconstruction 33613.5. Example of myocardial SPECT 34313.6. Conclusion 34613.7. Bibliography 348Chapter 14. Positron Emission Tomography 351Michel DEFRISE and Régine TRÉBOSSEN14.1. Introduction 35114.2. Data acquisition 35314.3. Data processing 36314.4. Research and clinical applications of PET 37014.5. Conclusion 37314.6. Bibliography 374Chapter 15. Functional Magnetic Resonance Imaging 377Christoph SEGEBARTH andMichel DÉCORPS15.1. Introduction 37715.2. Functional MRI of cerebrovascular responses 37815.3. fMRI of BOLD contrasts 38015.4. Different protocols 38315.5. Bibliography 389Chapter 16. Tomography of Electrical Cerebral Activity in Magneto- and Electro-encephalography 393Line Garnero16.1. Introduction 39316.2. Principles of MEG and EEG 39416.3. Imaging of electrical activity of the brain based on MEG and EEG signals 39816.4. Conclusion 40716.5. Bibliography 408List of Authors 411Index 417