Medical Image Reconstruction A Conceptual Tutorial
"Medical Image Reconstruction: A Conceptual Tutorial" introduces the classical and modern image reconstruction technologies, such as two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-bea
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Gengsheng Lawrence Zeng
Medical Image Reconstruction A Conceptual Tutorial
With 163 Figures
Author Prof. Dr. Gengsheng Lawrence Zeng Utah Center for Advanced Imaging Research Department of Radiology University of Utah Salt Lake City, UT 84108, USA E-mail: [email protected]
ISBN 978-7-04-020437-7 Higher Education Press, Beijing ISBN 978-3-642-05367-2
e-ISBN 978-3-642-05368-9
Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009937574 c Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Frido Steinen-Broo, EStudio Calamar, Spain Printed on acid-free paper Springer is part of Springer Science + Business Media (www.springer.com)
This book is dedicated to Ya, Andrew, Kathy, and Megan
Preface
The first time I heard about image reconstruction was twenty years ago I came to the University of Utah as a post-doctoral fellow in the Department of Radiology. Dr. Grant Gullberg and Dr. Rolf Clackdoyle gave many lectures on image reconstruction and I took notes. Even today I still go back to those notes from time to time. I benefit from those notes significantly. This book is complied together with parts of those notes and some current research papers with most mathematical proofs removed. I am grateful to Dr. Gullberg and Dr. Clackdoyle for introducing me to the wonderful world of image reconstruction. I appreciate Dr. Michel Defrise, Dr. Ge Wang, and Dr. Guang-Hong Chen for their helpful suggestions. I also like to thank my colleagues in the department and in other institutions. I would especially like to thank Kathy Gullberg and Jacob Piatt for proof-reading the drafts. This tutorial text introduces the classical and modern image reconstruction technologies to the general audience. It covers the topics in twodimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. Both analytical and iterative methods are presented. The applications in X-ray CT, SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging) are also discussed. Contemporary research results in exact RO
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