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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：
316.000千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2009-01-09
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.

  • 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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