Computed Tomography. Principles, Design, Artifacts, and Recent Advances. Jiang Hsieh THIRD EDITION. SPIE PRESS Bellingham, Washington USA

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1 Computed Tomography Principles, Design, Artifacts, and Recent Advances THIRD EDITION Jiang Hsieh SPIE PRESS Bellingham, Washington USA

2 Table of Contents Preface Nomenclature and Abbreviations xi xv 1 Introduction Conventional X-ray Tomography History of Computed Tomography Different Generations of CT Scanners Problems 21 References 21 2 Preliminaries Mathematics Fundamentals Fourier transform and convolution Random variables Linear algebra Fundamentals of X-ray Physics Production of x rays Interaction of x rays with matter Measurement of Line Integrals and Data Conditioning Sampling Geometry and Sinogram Problems 52 References 55 3 Image Reconstruction Introduction Several Approaches to Image Reconstruction The Fourier Slice Theorem The Filtered Backprojection Algorithm Derivation of the filtered backprojection formula Computer implementation Targeted reconstruction Fan-Beam Reconstruction Reconstruction formula for equiangular sampling Reconstruction formula for equal-spaced sampling Fan-beam to parallel-beam rebinning 99 v

3 vi Table of Contents 3.6 Iterative Reconstruction Mathematics versus reality The general approach to iterative reconstruction Algebraic reconstruction System modeling process Optimization algorithms Image quality benefit of MBIR Reconstruction speedup Problems 123 References Image Presentation CT Image Display Volume Visualization Multiplanar reformation MIP, minmip, and volume rendering Surface rendering D printing Impact of Visualization Tools Problems 156 References Key Performance Parameters of the CT Scanner High-Contrast Spatial Resolution In-plane resolution Slice sensitivity profile Low-Contrast Resolution Temporal Resolution CT Number Accuracy and Noise Impact of Iterative Reconstruction on Performance Measurement Performance-metric-based approach Task-based approach Surrogate task with clinical data Surrogate task with nonclinical data Performance of the Scanogram Problems 203 References Major Components of the CT Scanner System Overview The X-ray Tube and High-Voltage Generator The X-Ray Detector and Data-Acquisition Electronics The Gantry and Slip Ring Collimation and Filtration 235

4 Table of Contents vii 6.6 The Reconstruction Engine The Patient Table Problems 241 References Image Artifacts: Appearances, Causes, and Corrections What Is an Image Artifact? Different Appearances of Image Artifacts Artifacts Related to System Design Aliasing Partial volume Scatter Noise-induced streaks Artifacts Related to X-ray Tubes Off-focal radiation Tube arcing Tube rotor wobble Detector-Induced Artifacts Offset, gain, nonlinearity, and radiation damage Primary speed and afterglow Detector response uniformity Patient-Induced Artifacts Patient motion Beam hardening Metal artifacts Incomplete projections Operator-Induced Artifacts Problems 339 References Computer Simulation and Analysis What Is Computer Simulation? Simulation Overview Simulation of Optics Computer Simulation of Physics-Related Performance Problems 371 References 372 COLOR PLATES 9 Helical or Spiral CT Introduction Clinical needs Enabling technology 379

5 viii Table of Contents 9.2 Terminology and Reconstruction Helical pitch Basic reconstruction approaches Selection of the interpolation algorithm and reconstruction plane Helical fan-to-parallel rebinning Slice Sensitivity Profile and Noise Helically Related Image Artifacts High-pitch helical artifacts Noise-induced artifacts System-misalignment-induced artifacts Helical artifacts caused by object slope Problems 419 References Multislice and Cone-beam CT The Need for Multislice CT Detector Configurations of Multislice and Cone-beam CT Nonhelical Mode of Reconstruction Helical Reconstruction Selection of interpolation samples Selection of region of reconstruction Reconstruction algorithms with 3D backprojection Multislice and Cone-beam Artifacts General description Cone-beam effects Interpolation-related image artifacts Noise-induced multislice and cone-beam artifacts Tilt artifacts in multislice and cone-beam helical CT Distortion in step-and-shoot mode SSP Artifacts due to geometric inaccuracy Comparison of multislice and single-slice helical CT Problems 477 References X-ray Radiation and Dose-Reduction Techniques Biological Effects of X-ray Radiation Measurement of X-ray Dose Terminology and the measurement standard Other measurement units and methods Issues with the current CTDI Methodologies for Dose Reduction Tube-current modulation Umbra-penumbra and overbeam issues 505

6 Table of Contents ix Physiological gating Organ-specific dose reduction Protocol optimization and impact of the operator Postprocessing techniques Advanced reconstruction Problems 520 References Advanced CT Applications Introduction Cardiac Imaging Coronary artery calcification (CAC) Coronary artery imaging (CAI) Data acquisition and reconstruction Temporal resolution improvement Spatial resolution improvement Dose and coverage CT Fluoroscopy CT Perfusion Screening and Quantitative CT Lung cancer screening Quantitative CT CT colonography Dual-Energy CT Intuitive explanation of DECT material differentiation Theory of basis material decomposition Monochromatic image generation Multimaterial differentiation DECT data acquisition Clinical applications of DECT Problems 610 References 613 Glossary 625 Index 633

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