Image Reconstruction: Applications in Medical Sciences

Gengsheng Lawrence Zeng

Published by De Gruyter 2017

Image Reconstruction

Applications in Medical Sciences

Gengsheng Lawrence Zeng

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110500592

Overview
Contents

About this book

This book introduces the classical and modern image reconstruction technologies. It covers topics in two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. Both analytical and iterative methods are presented. The applications in X-ray CT, SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging) are discussed. Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections, Katsevich’s cone-beam filtered backprojection algorithm, and reconstruction with highly under-sampled data are included.

The last chapter of the book is devoted to the techniques of using a fast analytical algorithm to reconstruct an image that is equivalent to an iterative reconstruction. These techniques are the author’s most recent research results.

This book is intended for students, engineers, and researchers who are interested in medical image reconstruction. Written in a non-mathematical way, this book provides an easy access to modern mathematical methods in medical imaging.

Table of Content:
Chapter 1 Basic Principles of Tomography
1.1 Tomography
1.2 Projection
1.3 Image Reconstruction
1.4 Backprojection
1.5 Mathematical Expressions
Problems
References
Chapter 2 Parallel-Beam Image Reconstruction
2.1 Fourier Transform
2.2 Central Slice Theorem
2.3 Reconstruction Algorithms
2.4 A Computer Simulation
2.5 ROI Reconstruction with Truncated Projections
2.6 Mathematical Expressions (The Fourier Transform and Convolution , The Hilbert Transform and the Finite Hilbert Transform , Proof of the Central Slice Theorem, Derivation of the Filtered Backprojection Algorithm , Expression of the Convolution Backprojection Algorithm, Expression of the Radon Inversion Formula ,Derivation of the Backprojection-then-Filtering Algorithm
Problems
References
Chapter 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 (Derivation of a Filtered Backprojection Fan-Beam Algorithm, A Fan-Beam Algorithm Using the Derivative and the Hilbert Transform)
Problems
References
Chapter 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
Problems
References
Chapter 5 3D Image Reconstruction
5.1 Parallel Line-Integral Data
5.2 Parallel Plane-Integral Data
5.3 Cone-Beam Data (Feldkamp's Algorithm, Grangeat's Algorithm, Katsevich's Algorithm)
5.4 Mathematical Expressions (Backprojection-then-Filtering for Parallel Line-Integral Data, Filtered Backprojection Algorithm for Parallel Line-Integral Data, 3D Radon Inversion Formula, 3D Backprojection-then-Filtering Algorithm for Radon Data, Feldkamp's Algorithm, Tuy's Relationship, Grangeat's Relationship, Katsevich’s Algorithm)
Problems
References
Chapter 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 (Analytical Methods, Iterative Methods, Iterative Methods)
6.7 Noise Modeling as a Likelihood Function
6.8 Including Prior Knowledge
6.9 Mathematical Expressions (ART, Conjugate Gradient Algorithm, ML-EM, OS-EM, Green’s One-Step Late Algorithm, Matched and Unmatched Projector/Backprojector Pairs )
6.10 Reconstruction Using Highly Undersampled Data with l0 Minimization
Problems
References
Chapter 7 MRI Reconstruction
7.1 The 'M'
7.2 The 'R'
7.3 The 'I'; (To Obtain z-Information, x-Information, y-Information)
7.4 Mathematical Expressions
Problems
References
Indexing

Presents analytical and iterative methods for medical images reconstruction.
Discusses algorithms and applications in X-ray CT, SPECT, PET and MRI.
Easy to follow and also suitable for medical graduate students.

Author / Editor information

Gengsheng Lawrence Zeng, Weber State University, Odgen, US

Reviews

"The structure and exposition are very good. Each chapter has a one-page summary that really does capture all the key points of the chapter. There are good explanations of all the scanning methods and how the physics works and how they are implemented. The book gives several alternate algorithms for processing the data, and gives good explanations of their strengths and weaknesses." MAA Reviews

Topics

Frontmatter Publicly Available Download PDF	I
Preface Requires Authentication Unlicensed Licensed Download PDF	VII
Contents Publicly Available Download PDF	IX
1. Basic principles of tomography Requires Authentication Unlicensed Licensed Download PDF	1
2. Parallel-beam image reconstruction Requires Authentication Unlicensed Licensed Download PDF	19
3. Fan-beam image reconstruction Requires Authentication Unlicensed Licensed Download PDF	50
4. Transmission and emission tomography Requires Authentication Unlicensed Licensed Download PDF	69
5. Three-dimensional image reconstruction Requires Authentication Unlicensed Licensed Download PDF	91
6. Iterative reconstruction Requires Authentication Unlicensed Licensed Download PDF	127
7. MRI reconstruction Requires Authentication Unlicensed Licensed Download PDF	178
8. Using FBP to perform iterative reconstruction Requires Authentication Unlicensed Licensed Download PDF	196
Index Requires Authentication Unlicensed Licensed Download PDF	221

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students in electrical engineering, computer science and medical science, biomedical engineers.
Pages
- Front matter: 14
- Main content: 226
Illustrations
- Illustrations: 50
- Tables: 10

eBook

Published: March 20, 2017
ISBN: 9783110500592