Computed Radiation Imaging

1st Edition

Physics and Mathematics of Forward and Inverse Problems

Authors: Esam Hussein
Hardcover ISBN: 9780123877772
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-


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About the Author

Esam Hussein

Affiliations and Expertise

University of New Brunswick, Fredericton, NB Canada