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医学图像重建 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

医学图像重建 英文
  • (美)Gengsheng Lawrence Zeng 著
  • 出版社: 北京:高等教育出版社
  • ISBN:9787040204377
  • 出版时间:2009
  • 标注页数:198页
  • 文件大小:24MB
  • 文件页数:210页
  • 主题词:医学图像-图像处理-英文

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图书目录

1 Basic Principles of Tomography1

1.1 Tomography1

1.2 Projection3

1.3 Image Reconstruction6

1.4 Backprojection8

1.5 Mathematical Expressions10

1.5.1 Projection10

1.5.2 Backprojection11

1.5.3 The Dirac δ-function12

1.6 Worked Examples14

1.7 Summary17

Problems18

References19

2 Parallel-Beam Image Reconstruction21

2.1 Fourier Transform21

2.2 Central Slice Theorem22

2.3 Reconstruction Algorithms25

2.3.1 Method 125

2.3.2 Method 226

2.3.3 Method 327

2.3.4 Method 428

2.3.5 Method 528

2.4 A Computer Simulation30

2.5 ROI Reconstruction with Truncated Projections31

2.6 Mathematical Expressions36

2.6.1 The Fourier Transform and Convolution36

2.6.2 The Hilbert Transform and the Finite Hilbert Transform36

2.6.3 Proof of the Central Slice Theorem39

2.6.4 Derivation of the Filtered Backprojection Algorithm40

2.6.5 Expression of the Convolution Backprojection Algorithm41

2.6.6 Expression of the Radon Inversion Formula41

2.6.7 Derivation of the Backprojection-then-Filtering Algorithm41

2.7 Worked Examples42

2.8 Summary45

Problems46

References46

3 Fan-Beam Image Reconstruction49

3.1 Fan-Beam Geometry and Point Spread Function49

3.2 Parallel-Beam to Fan-Beam Algorithm Conversion52

3.3 Short Scan54

3.4 Mathematical Expressions56

3.4.1 Derivation of a Filtered Backprojection Fan-Beam Algorithm57

3.4.2 A Fan-Beam Algorithm Using the Derivative and the Hilbert Transform58

3.5 Worked Examples60

3.6 Summary63

Problems64

References65

4 Transmission and Emission Tomography67

4.1 X-Ray Computed Tomography67

4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography71

4.3 Attenuation Correction for Emission Tomography75

4.4 Mathematical Expressions79

4.5 Worked Examples81

4.6 Summary83

Problems83

References84

5 3D Image Reconstruction87

5.1 Parallel Line-Integral Data87

5.1.1 Backprojection-then-Filtering90

5.1.2 Filtered Backprojection91

5.2 Parallel Plane-Integral Data92

5.3 Cone-Beam Data94

5.3.1 Feldkamp's Algorithm95

5.3.2 Grangeat's Algorithm96

5.3.3 Katsevich's Algorithm97

5.4 Mathematical Expressions101

5.4.1 Backprojection-then-Filtering for Parallel Line-Integral Data102

5.4.2 Filtered Backprojection Algorithm for Parallel Line-Integral Data103

5.4.3 3D Radon Inversion Formula104

5.4.4 3D Backprojection-then-Filtering Algorithm for Radon Data104

5.4.5 Feldkamp's Algorithm105

5.4.6 Tuy's Relationship106

5.4.7 Grangeat's Relationship108

5.4.8 Katsevich's Algorithm111

5.5 Worked Examples117

5.6 Summary119

Problems120

References121

6 Iterative Reconstruction125

6.1 Solving a System of Linear Equations125

6.2 Algebraic Reconstruction Technique130

6.3 Gradient Descent Algorithms131

6.4 Maximum-Likelihood Expectation-Maximization Algorithms134

6.5 Ordered-Subset Expectation-Maximization Algorithm135

6.6 Noise Handling136

6.6.1 Analytical Methods—Windowing136

6.6.2 Iterative Methods—Stopping Early137

6.6.3 Iterative Methods——Choosing Pixels138

6.6.4 Iterative Methods—Accurate Modeling140

6.7 Noise Modeling as a Likelihood Function141

6.8 Including Prior Knowledge143

6.9 Mathematical Expressions145

6.9.1 ART145

6.9.2 Conjugate Gradient Algorithm146

6.9.3 ML-EM148

6.9.4 OS-EM151

6.9.5 Green's One-Step Late Algorithm151

6.9.6 Matched and Unmatched Projector/Backprojector Pairs151

6.10 Reconstruction Using Highly Undersampled Data with l0 Minimization153

6.11 Worked Examples156

6.12 Summary167

Problems168

References170

7 MRI Reconstruction175

7.1 The"M"175

7.2 The"R"177

7.3 The"I"180

7.3.1 To Obtain z-Information—Slice Selection180

7.3.2 To Obtain x-Information—Frequency Encoding182

7.3.3 To Obtain y-Information—Phase Encoding183

7.4 Mathematical Expressions185

7.5 Worked Examples188

7.6 Summary190

Problems191

References192

Index193

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