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基本説明
Provides a firm foundation in the mathematical tools at the heart of medical imaging technology.
Full Description
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts, and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.
This text uses X-ray computed tomography as a ""pedagogical machine"" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI.
Contents
Preface to the Second Edition
Preface
How to Use This Book
Notational Conventions
Chapter 1: Measurements and Modeling
Chapter 2: Linear Models and Linear Equations
Chapter 3: A Basic Model for Tomography
Chapter 4: Introduction to the Fourier Transform
Chapter 5: Convolution
Chapter 6: The Radon Transform
Chapter 7: Introduction to Fourier Series
Chapter 8: Sampling
Chapter 9: Filters
Chapter 10: Implementing Shift Invariant Filters
Chapter 11: Reconstruction in X-Ray Tomography
Chapter 12: Imaging Artifacts in X-Ray Tomography
Chapter 13: Algebraic Reconstruction Techniques
Chapter 14: Magnetic Resonance Imaging
Chapter 15: Probability and Random Variables
Chapter 16: Applications of Probability
Chapter 17: Random Processes
Appendix A: Background Material
Appendix B: Basic Analysis
Index.
