Introduction to the Mathematics of Medical Imaging

At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.

Charles L. Epstein is a Professor at the University of Pennsylvania with appointments in mathematics and radiology. He works in numerical analysis, magnetic resonance imaging, and image analysis, and has also worked in a variety of fields of mathematical analysis connected to partial differential equations and several complex variables. Professor Epstein is on the editorial board of Inverse Problems and he is an editor of BirkhSuser's Cornerstones book series.