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Medical Image Reconstruction: A Conceptual Tutorial（医学图像重建）

样章
作者：
Gengsheng Lawrence Zeng
定价：
38.00 元
版面字数：
316千字
开本：
16开
装帧形式：
精装
页数：
198
最新
印次时间：
2009年01月
ISBN：
978-7-04-020437-7
物料号：
20437-00
出版时间：
2009-11-03
读者对象：
学术著作
一级分类：
自然科学
二级分类：
信息与通信工程
三级分类：
信号与信息处理

Medical Image Reconstruction A Conceptual Tutorial introduces the classical and modern image reconstruction technologies, such as two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. This book presents both analytical and iterative methods of these technologies and their applications in X-ray CT (computed tomography), SPECT (single photon emission computed tomography), PET (positron emission tomography),and MRI (magnetic resonance imaging). Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections,Katsevich's cone-beam filtered backprojection algorithm, and reconstruction with highly undersampled data with/o-minimization are also included.

This book is written for engineers and researchers in the field of biomedical engineering specializing in medical imaging and image processing with image reconstruction.

  • 目录
    • Front Matter
      • 1 Basic Principles of Tomography
        • 1.1 Tomography
          • 1.2 Projection
            • 1.3 Image Reconstruction
              • 1.4 Backprojection
                • *1.5 Mathematical Expressions
                  • 1.5.1 Projection
                    • 1.5.2 Backprojection
                      • 1.5.3 The Dirac δ-function
                      • 1.6 Worked Examples
                        • 1.7 Summary
                          • Problems
                            • References
                            • 2 Parallel-Beam Image Reconstruction.
                              • 2.1 Fourier Transform
                                • 2.2 Central Slice Theorem
                                  • 2.3 Reconstruction Algorithms
                                    • 2.3.1 Method 1
                                      • 2.3.2 Method 2
                                        • 2.3.3 Method 3
                                          • 2.3.4 Method 4
                                            • 2.3.5 Method 5
                                            • 2.4 A Computer Simulation
                                              • *2.5 ROI Reconstruction with Truncated Projections
                                                • *2.6 Mathematical Expressions
                                                  • 2.6.1 The Fourier Transform and Convolution
                                                    • 2.6.2 The Hilbert Transform and the Finite Hilbert Transform
                                                      • 2.6.3 Proof of the Central Slice Theorem
                                                        • 2.6.4 Derivation of the Filtered Backprojection Algorithm
                                                          • 2.6.5 Expression of the Convolution Backprojection Algorithm
                                                            • 2.6.6 Expression of the Radon Inversion Formula
                                                              • 2.6.7 Derivation of the Backprojection-then-Filtering Algorithm
                                                              • 2.7 Worked Examples
                                                                • 2.8 Summary
                                                                  • Problems
                                                                    • References
                                                                    • 3 Fan-Beam Image Reconstruction
                                                                      • 3.1 Fan-Beam Geometry and Point Spread Function
                                                                        • 3.2 Parallel-Beam to Fan-Beam Algorithm Conversion
                                                                          • 3.3 Short Scan
                                                                            • *3.4 Mathematical Expressions
                                                                              • 3.4.1 Derivation of a Filtered Backprojection Fan-Beam Algorithm
                                                                                • 3.4.2 A Fan-Beam Algorithm Using the Derivative and the Hilbert Transform
                                                                                • 3.5 Worked Examples
                                                                                  • 3.6 Summary
                                                                                    • Problems
                                                                                      • References
                                                                                      • 4 Transmission and Emission Tomography
                                                                                        • 4.1 X-Ray Computed Tomography
                                                                                          • 4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography
                                                                                            • 4.3 Attenuation Correction for Emission Tomography
                                                                                              • *4.4 Mathematical Expressions
                                                                                                • 4.5 Worked Examples
                                                                                                  • 4.6 Summary
                                                                                                    • Problems
                                                                                                      • References
                                                                                                      • 5 3D Image Reconstruction
                                                                                                        • 5.1 Parallel Line-Integral Data
                                                                                                          • 5.1.1 Backprojection-then-Filtering
                                                                                                            • 5.1.2 Filtered Backprojection
                                                                                                            • 5.2 Parallel Plane-Integral Data
                                                                                                              • 5.3 Cone-Beam Data
                                                                                                                • 5.3.1 Feldkamp's Algorithm
                                                                                                                  • 5.3.2 Grangeat's Algorithm
                                                                                                                    • 5.3.3 Katsevich's Algorithm
                                                                                                                    • *5.4 Mathematical Expressions
                                                                                                                      • 5.4.1 Backprojection-then-Filtering for Parallel Line-Integral Data
                                                                                                                        • 5.4.2 Filtered Backprojection Algorithm for Parallel Line-Integral Data
                                                                                                                          • 5.4.3 3D Radon Inversion Formula
                                                                                                                            • 5.4.4 3D Backprojection-then-Filtering Algorithm for Radon Data
                                                                                                                              • 5.4.5 Feldkamp's Algorithm
                                                                                                                                • 5.4.6 Tuy's Relationship
                                                                                                                                  • 5.4.7 Grangeat's Relationship
                                                                                                                                    • 5.4.8 Katsevich's Algorithm
                                                                                                                                    • 5.5 Worked Examples
                                                                                                                                      • 5.6 Summary
                                                                                                                                        • Problems
                                                                                                                                          • References
                                                                                                                                          • 6 Iterative Reconstruction
                                                                                                                                            • 6.1 Solving a System of Linear Equations
                                                                                                                                              • 6.2 Algebraic Reconstruction Technique
                                                                                                                                                • 6.3 Gradient Descent Algorithms
                                                                                                                                                  • 6.4 Maximum-Likelihood Expectation-Maximization Algorithms
                                                                                                                                                    • 6.5 Ordered-Subset Expectation-Maximization Algorithm
                                                                                                                                                      • 6.6 Noise Handling
                                                                                                                                                        • 6.6.1 Analytical Methods — Windowing
                                                                                                                                                          • 6.6.2 Iterative Methods — Stopping Early
                                                                                                                                                            • 6.6.3 Iterative Methods — Choosing Pixels
                                                                                                                                                              • 6.6.4 Iterative Methods — Accurate Modeling
                                                                                                                                                              • 6.7 Noise Modeling as a Likelihood Function
                                                                                                                                                                • 6.8 Including Prior Knowledge
                                                                                                                                                                  • *6.9 Mathematical Expressions
                                                                                                                                                                    • 6.9.1 ART
                                                                                                                                                                      • 6.9.2 Conjugate Gradient Algorithm
                                                                                                                                                                        • 6.9.3 ML-EM
                                                                                                                                                                          • 6.9.4 OS-EM
                                                                                                                                                                            • 6.9.5 Green's One-Step Late Algorithm
                                                                                                                                                                              • 6.9.6 Matched and Unmatched Projector/Backprojector Pairs
                                                                                                                                                                              • *6.10 Reconstruction Using Highly Undersampled Data with l0 Minimization
                                                                                                                                                                                • 6.11 Worked Examples
                                                                                                                                                                                  • 6.12 Summary
                                                                                                                                                                                    • Problems
                                                                                                                                                                                      • References
                                                                                                                                                                                      • 7 MRI Reconstruction
                                                                                                                                                                                        • 7.1 The "M"
                                                                                                                                                                                          • 7.2 The "R"
                                                                                                                                                                                            • 7.3 The "I"
                                                                                                                                                                                              • 7.3.1 To Obtain z-Information—Slice Selection
                                                                                                                                                                                                • 7.3.2 To Obtain x-Information—Frequency Encoding
                                                                                                                                                                                                  • 7.3.3 To Obtain y-Information— Phase Encoding
                                                                                                                                                                                                  • *7.4 Mathematical Expressions
                                                                                                                                                                                                    • 7.5 Worked Examples
                                                                                                                                                                                                      • 7.6 Summary
                                                                                                                                                                                                        • Problems
                                                                                                                                                                                                          • References
                                                                                                                                                                                                          • Index

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