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 imaging modalities in current use. In the process, it also covers many important analytic concepts and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.
This text uses X-ray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat s formula, an improved description of the gridding method, and a new section on noise analysis in MRI.
Audience The book is appropriate for one- or two-semester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis.
This book provides a firm foundation in the mathematical tools used to model the measurements at the heart of medical imaging technology, and now includes a new chapter on magnetic resonance imaging (MRI). Extensive background material, over 200 illustrations and numerous exercises make these advanced mathematical topics more accessible.
About the Author
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 BirkhÃ¤user s Cornerstones book series.