Kuckment describes the main problems and techniques of some well-established imaging modalities, emphasizes the most important mathematical ideas involved, and briefly summarizes several imaging techniques that are less common and/or currently being developed. He focuses mostly but not exclusively on modalities allowing integral geometry approaches. Among his topics are some major computed tomography (CT) modalities and their features to watch for, emission tomography, three-dimensional radon and X-ray transforms, ultrasound modulation in electrical impedance tomography (EIT) and optical tomography (OT), and inverse problems with interior information. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
A guide to the mathematical ideas and techniques behind medical imaging modalities, suitable for researchers and graduate students.
Preface
Part I:
Chapter 1: Introduction
Part II: Traditional Tomographic Techniques and Integral Geometry
Chapter 2: Tomography and Radon Transform
Chapter 3: Emission Tomography
Chapter 4: Microlocal Analysis
Chapter 5: More About 3D Radon and X-Ray Transforms
Chapter 6: Numerical Methods
Chapter 7: Various Other Modalities
Part III: Hybrid Imaging
Chapter 8: Thermoacoustics
Chapter 9: Ultrasound Modulation
Chapter 10:Hybrid Miscellany
Chapter 11: Inverse Problems and Internal Information
Part IV: Appendices
Appendix A: Notations
Appendix B: Fourier Analysis
Appendix C: Geometric Rays, Trapping, Energy Decay
Appendix D: Fredholm Operator Functions
Appendix E: Books and Survey Recommendations
Bibliography
Index.
Peter Kuchment is a Distinguished Professor in the Mathematics Department of Texas A&M University. He is a Fellow of both the American Mathematical Society and the Institute of Physics. His work is focused in the areas of mathematical physics, partial differential equations, spectral theory, medical imaging, and the enhancement of K-12 education in mathematics. He has authored more than 150 publications, including the books Floquet Theory for Partial Differential Equations (1993) and Introduction to Quantum Graphs (with G. Berkolaiko, 2013).
