Download Introduction to the Mathematics of Medical Imaging, Second Edition Book

Introduction to the Mathematics of Medical Imaging, Second Edition


Book Title :Introduction to the Mathematics of Medical Imaging, Second Edition

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 Xray 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. Audience The book is appropriate for one or twosemester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis. 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 XRay Tomography Chapter 12: Imaging Artifacts in XRay 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.



Author(s) Book :Charles L. Epstein (2007)

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