The Mathematics of Medical Imaging: A Beginner's Guide

This is a mathematics book. It is not a "math for the math-averse" book, and it is not a numerical methods book. It is a textbook that presents a compact, rigorous treatment of basic tomographic image reconstruction at a level suitable for an undergraduate who is strong in math. The chapters address x-rays, the Radon transform, backprojection, complex numbers, the Fourier transform, the Central Slice Theorem, filtered backprojection and the Hilbert transform, filters and convolution, sampled data and discrete image reconstruction, algebraic reconstruction techniques, and MRI. Appendices provide background information on integrability and a list of topics for further study. The text deals primarily with a single-slice, parallel-beam geometry. It discusses the Radon transform and filtered backprojection in great detail. It also has a nice section on algebraic reconstruction techniques, as they are illustrative of interesting mathematics, even if not widely used in modern practice.

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