The Mathematics of Medical Imaging [electronic resource] : A Beginner's Guide / by Timothy G. Feeman.

X-rays -- The Radon Transform -- Back Projection -- Complex Numbers -- The Fourier Transform -- Two Big Theorems -- Filters and Convolution -- Discrete Image Reconstruction -- Algebraic Reconstruction Techniques -- MRI-An Overview.

A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography - the CT scan - 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 are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. The text is self-contained with a range of practical exercises, topics for further study, and an ample bibliography, making it ideal for use in an undergraduate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of their field.