Winner of the 2006 Joseph W. Goodman Book Writing Award!

A comprehensive treatment of the principles, mathematics, and statistics of image science

In today's visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world.

Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and statistics needed to understand and evaluate imaging systems. The book is the first to provide a thorough treatment of the continuous-to-discrete, or CD, model of digital imaging. Foundations of Image Science emphasizes the need for meaningful, objective assessment of image quality and presents the necessary tools for this purpose. Approaching the subject within a well-defined theoretical and physical context, this landmark text presents the mathematical underpinnings of image science at a level that is accessible to graduate students and practitioners working with imaging systems, as well as well-motivated undergraduate students.

Destined to become a standard text in the field, Foundations of Image Science covers:

* Mathematical Foundations: Examines the essential mathematical foundations of image science

* Image Formation-Models and Mechanisms: Presents a comprehensive and unified treatment of the mathematical and statistical principles of imaging, with an emphasis on digital imaging systems and the use of SVD methods

* Image Quality: Provides a systematic exposition of the methodology for objective or task-based assessment of image quality

* Applications: Presents detailed case studies of specific direct and indirect imaging systems and provides examples of how to apply the various mathematical tools covered in the book

* Appendices: Covers the prerequisite material necessary for understanding the material in the main text, including matrix algebra, complex variables, and the basics of probability theory

HARRISON H. BARRETT received a BS in physics from Virginia
Polytechnic Institute, an MS in Physics from MIT, and a PhD in
applied physics from Harvard. Dr. Barrett is a professor in the
Optical Sciences Center, the Department of Radiology, and the
Program in Applied Mathematics and serves as Director of the Center
for Gamma-ray Imaging. The holder of twenty-three U.S. patents, he
is the recipient of the IEEE Medical Imaging Scientist Award and a
Humboldt Prize and the coauthor, with William Swindell, of
Radiological Imaging: The Theory of Image Formation, Detection,
and Processing.

KYLE J. MYERS received a BS in Mathematics and Physics
from Occidental College and an MS and PhD in Optical Sciences from
the University of Arizona. Dr. Myers is the Chief of the Medical
Imaging and Computer Applications Branch of the Center for Devices
and Radiological Health of the U.S. Food and Drug Administration.
She is a member of the SPIE, the Optical Society of America, and
the Medical Image Perception Society (MIPS), and recently served as
cochair of the Medical Image Perception Conference sponsored by
MIPS.

Winner of the 2006 Joseph W. Goodman Book Writing Award!

A comprehensive treatment of the principles, mathematics, and statistics of image science

In today's visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world.

Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and statistics needed to understand and evaluate imaging systems. The book is the first to provide a thorough treatment of the continuous-to-discrete, or CD, model of digital imaging. Foundations of Image Science emphasizes the need for meaningful, objective assessment of image quality and presents the necessary tools for this purpose. Approaching the subject within a well-defined theoretical and physical context, this landmark text presents the mathematical underpinnings of image science at a level that is accessible to graduate students and practitioners working with imaging systems, as well as well-motivated undergraduate students.

Destined to become a standard text in the field, Foundations of Image Science covers:

• Mathematical Foundations: Examines the essential mathematical foundations of image science
• Image FormationModels and Mechanisms: Presents a comprehensive and unified treatment of the mathematical and statistical principles of imaging, with an emphasis on digital imaging systems and the use of SVD methods
• Image Quality: Provides a systematic exposition of the methodology for objective or task-based assessment of image quality
• Applications: Presents detailed case studies of specific direct and indirect imaging systems and provides examples of how to apply the various mathematical tools covered in the book
• Appendices: Covers the prerequisite material necessary for understanding the material in the main text, including matrix algebra, complex variables, and the basics of probability theory

1.1 LINEAR VECTOR SPACES.

1.1.1 Vector addition and scalar multiplication.

1.1.2 Metric spaces and norms.

1.1.3 Sequences of vectors and complete metric spaces.

1.1.4 Scalar products and Hilbert space.

1.1.5 Basis vectors.

1.1.6 Continuous bases.

1.2 TYPES OF OPERATORS.

1.2.1 Functions and functionals.

1.2.2 Integral transforms.

1.2.3 Matrix operators.

1.2.4 Continuous-to-discrete mappings.

1.2.5 Differential operators.

1.3 HILBERT-SPACE OPERATORS.

1.3.1 Range and domain.

1.3.2 Linearity, boundedness and continuity.

1.3.3 Compactness.

1.3.4 Inverse operators.

1.3.5 Adjoint operators.

1.3.6 Projection operators.

1.3.7 Outer products.

1.4 EIGENANALYSIS.

1.4.1 Eigenvectors and eigenvalue spectra.

1.4.2 Similarity transformations.

1.4.3 Eigenanalysis infinite-dimensional spaces.

1.4.4 Eigenanalysis of Hermitian operators.

1.4.5 Diago nalization of a Hermitian operator.

1.4.6 Simultaneo us diagonalization of Hermitian matrices.

1.5 SINGULAR-VALUE DECOMPOSITION.

1.5.1 Definition and properties.

1.5.2 Subspaces.

1.5.3 SVD representation of vectors and operators.

1.6 MOORE-PENROSE PSEUDOINVERSE.

1.6.1 Penrose equations.

1.6.2 Pseudoinverses and SVD.

1.6.3 Properties of the pseudoinverse.

1.6.4 Pseudoinverses and projection operators.

1.7 PSEUDOINVERSES AND LINEAR EQUATIONS.

1.7.1 Nature of solutions of linear equations.

1.7.2 Existence and uniqueness of exact solutions.

1.7.3 Explicit solutions for consistent data.

1.7.4 Least-squares solutions.

1.7.5 Minimum-norm solutions.

1.7.6 Iterative calculation of pseudoinverse solution.

1.8 REPRODUCING-KERNEL HILBERT SPACES.

1.8.1 Positive-definite Hermitian operators.

1.8.2 Nonnegative-definite Hermitian operators.

2. THE DIRAC DELTA AND OTHER GENERALIZED FUNCTIONS.

2.1 THEORY OF DISTRIBUTIONS.

2.1.1 Basic concepts.

2.1.2 Well-behaved functions.

2.1.3 Approximation of other functions.

2.1.4 Formal definition of distributions.

2.1.5 Properties of distributions.

2.1.6 Tempered distributions.

2.2 ONE-DIMENSIONAL DELTA FUNCTION.

2.2.1 Intuitive …