The Radon Transform and Medical Imaging

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).

List of figures; Preface; Part I. Introduction: 1. Why use mathematics in medical imaging?; 2. A brief and incomplete history of CT; 3. Some major CT modalities and their features to watch for; 4. Organization of the book; Part II. Traditional Computed Tomography Techniques and Integral Geometry: 5. 'Standard' CT and X-ray and Radon transforms; 6. Emission tomography; 7. Artifacts, incomplete data, microlocal analysis, and such; 8. More about 3D Radon and X-ray transforms; 9. A brief overview of numerical methods; 10. MRI, EIT, OT, elastography, UT; Part III. Hybrid (Coupled Physics) Imaging Techniques: 11. Thermo-, photo-, and optoacoustic tomography (TAT/PAT/OAT); 12. Ultrasound modulation in EIT and OT; 13. Inverse problems with interior information; Part IV. Appendices: A. Notation; B. Brief notes on the Fourier transform and harmonic analysis; C. Geometric rays, trapping, energy decay; D. Some classes of linear operators and operator functions; E. Recommended books and surveys; Bibliography; Index.