The Mathematics of Medical Imaging A Beginner’s Guide /

• Main Author: Feeman, Timothy G. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Edition: 2nd ed. 2015.
• Series: Springer Undergraduate Texts in Mathematics and Technology,
• Subjects: Mathematics.; Radiology.; Computer science > Mathematics.; Computer graphics.; Functional analysis.; Integral transforms.; Operational calculus.; Biomedical engineering.; Functional Analysis.; Imaging / Radiology.; Computer Imaging, Vision, Pattern Recognition and Graphics.; Biomedical Engineering.; Integral Transforms, Operational Calculus.; Math Applications in Computer Science.

The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms a...

Table of Contents:

• 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.