Mathematics and Physics of Emerging Biomedical Imaging -- Copyright -- PREFACE -- Contents -- Chapter 1 Introduction and Summary -- PLATE CAPTIONS -- Chapter 2 X-Ray Projection Imaging -- 2.1 INTRODUCTION -- 2.2 MAMMOGRAPHY -- 2.2.1 Scanning Methods -- 2.2.2 Area Detectors -- 2.3 CHEST RADIOGRAPHY -- 2.3.1 Scanning Methods -- 2.3.2 Area Detectors -- 2.4 DIGITAL FLUOROSCOPY -- 2.5 PORTAL IMAGING -- 2.6 RESEARCH OPPORTUNITIES -- 2.7 Suggested Reading -- Chapter 3 X-Ray Computed Tomography -- 3.1 INTRODUCTION -- 3.1.1 History -- 3.1.2 Principle of Operation -- 3.2 PRESENT STATUS OF CT INSTRUMENTATION AND TECHNOLOGY -- 3.2.1 X-Ray Tubes -- 3.2.2 Detector Systems -- 3.2.3 Image Artifacts -- 3.2.4 Quantitative CT -- 3.2.5 Requirements for High-Speed CT -- 3.3 SPIRAL CT -- 3.4 ELECTRON BEAM TECHNIQUES -- 3.5 DATA HANDLING AND DISPLAY TECHNIQUES -- 3.6 RESEARCH OPPORTUNITIES -- 3.7 Suggested Reading -- Chapter 4 Magnetic Resonance Imaging -- 4.1 PRINCIPLES OF MAGNETIC RESONANCE IMAGING -- 4.2 HARDWARE -- 4.2.1 Magnet Systems: Current Status and Opportunities -- 4.2.2 Pulsed-field MRI Systems -- 4.2.3 Radio-frequency Coils for MRI -- Computational Design of RF Coils -- Cooled Receiver Coils for MR Imaging -- Use of Multiple Receivers -- 4.2.4 Magnetic Field Gradients -- Local versus Whole-Body Gradients -- Design Considerations -- Applications -- Bioeffects -- 4.2.5 Research Opportunities for MRI Hardware -- Magnet Systems -- Pulsed-field MRI -- RF Coils -- Gradient Systems -- 4.2.6 Suggested Reading Related to MRI Hardware -- Magnet Systems -- Pulsed-field MRI -- RF Coils -- Gradient Systems -- 4.3 DYNAMIC MR IMAGE RECONSTRUCTION -- 4.3.1 Partial Fourier Reconstruction -- Predominantly One-sided Data Collection -- Predominantly Every Other Point -- Collecting Multiple Echoes -- Two- and Three-Dimensional Extensions -- 4.3.2 Reduced Gibbs Ringing.

Iterative Sigma Filtering -- Constraint-based Methods -- Parametric Estimation -- 4.3.3 High-speed K-space Coverage Techniques -- 4.3.4 Research Opportunities in Dynamic MR Image Reconstruction -- 4.3.5 Suggested Reading Related to Dynamic MR Image Reconstruction -- 4.4 APPLICATIONS OF DYNAMIC MRI -- 4.4.1 Blood Flow -- Fourier Velocity Encoding -- RF Pulses -- Measurement of Wave Speed and Distensibility -- Postprocessing -- Conclusions Related to MR Imaging of Blood Flow -- 4.4.2 Diffusion Imaging -- Measurement of Diffusion Coefficients in vivo -- Mapping of Diffusion Tensor -- 4.4.3 Other Tissue Parameters -- Relaxation Times -- Oxygen -- Strain -- 4.4.4 Functional Brain MRI -- Contrast Mechanism -- Imaging Techniques -- Hardware Requirements -- Field Strength Considerations As discussed above, local field gradients -- Processing of Functional Images -- Safety Considerations -- Biophysical Modeling -- 4.4.5 Multinuclear MRI -- MR Spectroscopy and Spectroscopic Imaging -- Injected Paramagnetic Contrast Agents and Hyperpolarized Noble Gases -- 4.4.6 Microscopic Imaging -- Resolution -- Signal-to-Noise Ratios -- Gradients -- Diffusion -- Motion -- Future Applications of in vivo MRI Microscopy -- 4.4.7 Research Opportunities Related to Applying Dynamic MRI -- Blood Flow -- Diffusion Imaging -- Other Tissue Parameters -- Functional Brain MRI -- Multinuclear MRI -- Microscopic Imaging -- 4.4.8 Suggested Reading on Applications of Dynamic MRI -- Blood Flow -- Diffusion Imaging -- Other Tissue Parameters -- Functional Brain MRI -- Multinuclear MRI -- Microscopic Imaging -- Chapter 5 Single Photon Emission Computed Tomography -- 5.1 INTRODUCTION -- 5.2 PHYSICAL AND INSTRUMENTATION FACTORS THAT AFFECT SPECT IMAGES -- 5.3 SPECT INSTRUMENTATION -- 5.3.1 SPECT System Designs -- 5.3.2 Special Collimators -- 5.3.3 New Radiation Detector Technologies.

5.4 SPECT IMAGE RECONSTRUCTION -- 5.4.1 The SPECT Reconstruction Problem -- 5.4.2 SPECT Image Reconstruction Methods -- Compensation Methods -- Three-Dimensional Reconstruction Methods for Special Collimator Designs -- 5.5 RESEARCH OPPORTUNITIES -- 5.6 Suggested Reading -- Chapter 6 Positron Emission Tomography -- 6.1 INTRODUCTION -- 6.1.1 History -- 6.1.2 Applications -- 6.1.3 Principle of Operation -- 6.2 CURRENT STATUS OF PET TECHNOLOGY -- 6.2.1 γ-Ray Detectors -- 6.2.2 Limitations of the Spatial Resolution -- 6.2.3 System Electronics -- 6.2.4 Data Correction and Reconstruction Algorithms -- 6.3 THREE-DIMENSIONAL ACQUISITION AND RECONSTRUCTION -- 6.3.1 Principle of Three-Dimensional Acquisition -- 6.3.2 Three-Dimensional Reconstruction -- 6.3.3 Scatter Correction in Three Dimensions -- 6.3.4 Attenuation Correction in Three Dimensions -- 6.4 RESEARCH OPPORTUNITIES -- 6.5 Suggested Reading -- Chapter 7 Ultrasonics -- 7.1 INTRODUCTION -- 7.2 INSTRUMENTATION -- 7.2.1 Transducers -- Field Distributions -- Acoustics and Vibration -- Electromechanical Properties of Ferroelectric Materials -- 7.2.2 Ultrasonic Beam Forming -- 7.2.3 Signal Processing -- 7.3 SCATTERING -- 7.4 ULTRASONIC TOMOGRAPHY -- 7.5 RESEARCH OPPORTUNITIES -- 7.6 Suggested Reading -- Chapter 8 Electrical Source Imaging -- 8.1 INTRODUCTION -- 8.2 OUTLINE OF ESI RECONSTRUCTION METHODS -- 8.2.1 Forward Problem -- 8.2.2 Inverse Problem -- 8.2.3 Temporal Regularization -- 8.3 RESEARCH PROBLEMS AND OPPORTUNITIES -- 8.4 Suggested Reading -- Chapter 9 Electrical Impedance Tomography -- 9.1 INTRODUCTION -- 9.2 COMPARISON TO OTHER MODALITIES -- 9.3 PRESENT STATUS OF EIT AND LIMITATIONS -- 9.4 RESEARCH OPPORTUNITIES -- 9.5 Suggested Reading -- Chapter 10 Magnetic Source Imaging -- 10.1 INTRODUCTION -- 10.2 MATHEMATICAL CONSIDERATIONS -- 10.3 SOURCE MODELS -- 10.4 RESOLUTION -- 10.5 SUMMARY.

10.6 RESEARCH OPPORTUNITIES -- 10.7 Suggested Reading -- Chapter 11 Medical Optical Imaging -- 11.1 INTRODUCTION -- 11.2 DATA ACQUISITION STRATEGIES -- 11.3 COMPARISONS WITH OTHER IMAGING MODALITIES -- 11.4 POSSIBLE APPLICATIONS OF OPTICAL TOMOGRAPHY -- 11.5 RESEARCH OPPORTUNITIES -- 11.6 Suggested Reading -- Chapter 12 Image-Guided Minimally Invasive Diagnostic and Therapeutic Interventional Procedures -- 12.1 THERAPEUTIC INTERVENTION EXPERIENCE WITH DIFFERENT IMAGING MODALITIES -- 12.1.1 X-Ray Imaging -- 12.1.2 Computed Tomography -- 12.1.3 Ultrasound -- 12.1.4 Endoscopy -- 12.1.5 Magnetic Resonance Imaging -- 12.2 THE ROLES OF IMAGING IN THERAPY -- 12.2.1 Planning -- 12.2.2 Guidance -- 12.2.3 Monitoring and Localization -- 12.2.4 Control -- 12.3 THERMAL SURGERY -- 12.3.1 Interstitial Laser Therapy -- 12.3.2 Cryotherapy -- 12.3.3 Focused Ultrasound -- 12.4 RESEARCH AND DEVELOPMENT OPPORTUNITIES -- Planning -- Guidance and Localization -- Monitoring -- Control -- Instruments and Systems -- 12.5 Suggested Reading -- Chapter 13 Frontiers of Image Processing for Medicine -- 13.1 IMAGE SEGMENTATION -- 13.2 COMPUTATIONAL ANATOMY -- 13.3 REGISTRATION OF MULTIMODALITY IMAGES -- 13.4 SYNTHESIS OF PARAMETRIC IMAGES -- 13.5 DATA VISUALIZATION -- 13.6 TREATMENT PLANNING -- 13.7 RESEARCH OPPORTUNITIES -- 13.8 Suggested Reading -- Chapter 14 A Cross-Cutting Look at the Mathematics of Emerging Biomedical Imaging -- 14.1 MATHEMATICAL MODELS FOR PARTICULAR IMAGING MODALITIES -- 14.1.1 Transmission Computed Tomography -- 14.1.2 Emission Computed Tomography -- 14.1.3 Ultrasound Computed Tomography -- 14.1.4 Optical Tomography -- 14.1.5 Electrical Impedance Tomography -- 14.1.6 Magnetic Resonance Imaging -- 14.1.7 Vector Tomography -- 14.1.8 Tensor Tomography -- 14.1.9 Magnetic Source Imaging -- 14.1.10 Electrical Source Imaging -- 14.2 FORWARD PROBLEMS.

14.3 INVERSE PROBLEMS -- 14.4 ILL-POSEDNESS AND REGULARIZATION -- 14.4.1 The Tikhonov-Phillips Method -- 14.4.2 The Truncated Singular Value Decomposition -- 14.4.3 Iterative Methods -- 14.4.4 Regularization by Discretization -- 14.4.5 Maximum Entropy -- 14.5 SAMPLING -- 14.5.1 Sampling in Real Space -- 14.5.2 Sampling in Fourier Space -- 14.6 PRIORS AND SIDE INFORMATION -- 14.7 RESEARCH OPPORTUNITIES -- 14.8 Suggested Reading -- Index.