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

Contents

• Vectors and operators
• The dirac delta and other generalized functions
• Fourier analysis
• Series expansions and integral transforms
• Mixed representations
• Group theory
• Deterministic descriptions of imaging systems
• Stochastic descriptions of objects and images
• Diffraction theory and imaging
• Energy transport and photons
• Poisson statistics and photon counting
• Noise in detectors
• Statistical decision theory
• Image quality
• Inverse problems
• Planar imaging with X rays and gamma rays
• Emission computed tomography
• Speckle
• Imaging in Fourier space
• Epilogue. Frontiers in image science
• Appendix A: Matrix Algebra
• Appendix B: Complex Variables
• Appendix C: Probability
• Bibliography
• Index