Mathematics of Medical Imaging

Timothy G. Feeman is professor of mathematics, Villanova University, in Lancaster, Pennsylvania. His original area of research is the theory of operators on Hilbert spaces once described as "the field of mathematics that has the strongest interaction with the scientific and technological developments which are characteristic of the twentieth century." Since the mid- to late-1990s, his scholarly efforts have become more diversified.

• Preface to Second Edition.-Preface.- 1. X-rays.- 2. The Radon Transform.- 3. Back Projection.- 4. Complex Numbers.- 5. The Fourier Transform.- 6. Two Big Theorems.- 7. Filters and Convolution.- 8. Discrete Image Reconstruction.- 9. Algebraic Reconstruction Techniques.- 10. MRI—An Overview.-Appendix A. Integrability.- Appendix B. Matrices, Transposes, and Factorization.- Appendix C.Topics for Further Study.- Bibliography.- Index.

"The text is concise, lucidly written and coherently structured. It is also self-contained and easily accessible to any undergraduate student having a solid command of mathematics at the level of some introductory courses in algebra and analysis. The code written in R is a genuine asset of high practical and educational value. Overall, this textbook provides good, highly informative, and useful material to students and all of those with interest in medical imaging." (Witold Pedrycz, zbMATH 1351.92002, 2017) "I believe that the book is a useful starting point for undergraduate students from mathematics, computer science, and related fields who want to learn how CT works; it also provides interesting reading for people from medical areas who want to find out the technical and mathematical background of the tools that they use." (Kai Diethelm, Computing Reviews, computingreviews.com, May, 2016)