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Computed Radiation Imaging - 1st Edition - ISBN: 9780123877772, 9780123877789

Computed Radiation Imaging

1st Edition

Physics and Mathematics of Forward and Inverse Problems

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Author: Esam Hussein
Hardcover ISBN: 9780123877772
Paperback ISBN: 9780323165297
eBook ISBN: 9780123877789
Imprint: Elsevier
Published Date: 27th May 2011
Page Count: 302
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Computer-assisted imaging with radiation (x- and gamma rays) is an integral part of modern medical-diagnostic practice. This imaging technology is also slowly finding its way into industrial applications. Although the technology is well developed, there is a need for further improvement to enhance image quality, reduce artifacts, minimize patient radiation exposure, compete with and complement other imaging methods (such as magnetic resonance imaging and ultrasonics), and accommodate dense and large objects encountered in industrial applications.

Scientists and engineers, attempting to progress this technology, are faced with an enormous amount of literature, addressing the imaging problem from various view points. This book provides a single source that addresses both the physical and mathematical aspects of the imaging problem in a consistent and comprehensive manner.

Key Features

  • Discusses the inherent physical and numerical capabilities and limitations of the methods presented for both the forward and inverse problems
  • Provides information on available Internet resources and software
  • Written in a manner that makes it readable by physicists, mathematicians, engineers and computer scientists – avoids, as much as possible, the use of specialized terminology without clear introduction and definition


Researchers working in the field of radiation-based imaging

Table of Contents


1. Radiation Imaging

1.1. Why Radiation?

1.2. Imaging Modalities

1.3. Direct and Reconstructed Imaging

1.4. The Forward and Inverse Problems

1.5. Forward and Inverse Mapping


2. Radiation Transport

2.1. Introduction

2.2. Variables

2.3. Cross Sections

2.4. Boltzmann Transport Equation

2.5. Source-Free Steady-State Problem

2.6. Steady-State Problem in Void

2.7. Point-Kernel Method

2.8. Charged Particles

3. Measurement Models

3.1. Formulation

3.2. Scaling

3.3. Measured Response

3.4. Sensitivity

3.5. Variability

3.6. Components

3.7. Image Grid

3.8. Idealization

3.9. Computer Coding

4. Transmission

4.1. Basic Model

4.2. Physical Relevance

4.3. Discretization

4.4. Nature of Radiation Source

4.5. Secondary Radiation

4.6. Scattering

4.7. Sensitivity

4.8. Variability

5. Emission

5.1. Embedded Radiation

5.2. Induced Emission

5.3. Discretization

5.4. Sensitivity

5.5. Sources

5.6. Interfering Effects

6. Scattering

6.1. Introduction

6.2. Single-Scattering Model

6.3. Multiple Scattering

6.4. Compton Scattering

6.5. Neutron Elastic Scattering

6.6. Discretization

6.7. Sensitivity


7. Features

7.1. Discretization

7.2. Well-Posed Problem

7.3. Existence

7.4. Uniqueness

7.5. Continuity

7.6. Ill-Posed Problem

7.7. Ill-Conditioning

7.A. Basics of Functional Analysis

8. Formulation

8.1. Matrix

8.2. Functional

8.3. Analytic

8.4. Probabilistic

8.A. Probabilistic Basis of Maximum-Likelihood and Least-Squares Methods

9. Preprocessing of Measurements

9.1. Number of Measurements

9.2. Frequency Analysis

9.3. Spatial Filtering of Noise

9.4. Consistency and Smoothing

10. Matrix-Based Methods

10.1. Error Propagation

10.2. Singular Value Decomposition

10.3. Least Squares

10.4. Regularization Methods

10.5. Regularization-Parameter Determination

10.6. Iterative Methods

10.7. Nonlinear Problems

10.8. Software

11. Functional Optimization

11.1. Formulation

11.2. Effect of Number of Measurements

11.3. Sensitivity to Measurement Uncertainty

11.4. Minimization

11.5. Search Methods

11.6. Genetic Evolution

11.7. Simulated Annealing

11.8. Neural Networks

12. Analytic Methods

12.1. Radon Transform

12.2. Two-Dimensional Fourier Transforms

12.3. Backprojection

12.4. Fan-Beam Transmission Tomography

12.5. Cone-Beam Transmission Tomography

12.6. Emission Imaging

12.7. Scatter Imaging

12.8. Computer Codes

12.9. Wavelet Transforms

13. Probabilistic Methods

13.1. Bayesian - Minimum Information

13.2. Poisson Distribution

13.3. Normal Distribution

13.4. Maximum a posteriori (map)

13.5. The Monte Carlo Method

14. Incomplete Problems

14.1. Incompleteness

14.2. General Solution Methods

14.3. Estimation Maximization

14.4. Markov Random Fields

15. Testing

15.1. Ideal Problem

15.2. Noisy-Ideal Problem

15.3. Independently-Simulated-Data Problem

15.4. Laboratory Problem

15.5. Image Quality

15.6. Test Objects

16. Post-Processing

16.1. Image Convolution

16.2. Image Degradation

16.3. Frequency Filtering

16.4. Matrix Based

16.5. Statistical Methods

16.6. Optimization

16.7. Blind Deconvolution



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© Elsevier 2011
27th May 2011
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About the Author

Esam Hussein

Affiliations and Expertise

University of New Brunswick, Fredericton, NB Canada

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