G.T. Herman F. Natterer Universitat des Saarlandes Medical Image Processing Group Department of Computer Science Angewandte Mathematik und State University of New York at Informatik 66 Saarbrucken Buffalo Germany 4226 Ridge Lea Road Amherst, N.Y. 14226 USA In August 1978 we have attended a working conference on Computer Aided Tomography and Ultrasonics in Medicine which was held in Haifa, Israel under the auspices of the International Federation for Information Pro cessing [1]. That meeting, in common with other meetings relating to computerized tomography, concentrated on the physical, engineering and clinical aspects of the topic, with little attention paid to the under lying mathematics, and no attention paid to recent developments in ma thematics inspired by computerized tomography (although not necessarily) useful for computerized tomography). We both felt that it would be worthwhile to organize a meeting of mathematicians which would concen trate on the mathematical aspects of computerized tomography. This vol ume (and the meeting on which it is based) is the outcome of our decision in August 1978 to attempt to bring together such a meeting. In the meantime much has been published on the topic of computerized to mography.

This book provides a unified view of tomographic techniques and an in-depth treatment of reconstruction algorithms.

The conference was devoted to the discussion of present and future techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic ima- ging. The mathematical models, their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scat- tering, inversion in 3D, and constrained least squares pro- blems.Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam recon- struction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applica- tions in non-medical fields. Contents: Theoretical Aspects: J.Boman: Helgason' s support theorem for Radon transforms-a newproof and a generalization -P.Maass: Singular value de- compositions for Radon transforms- W.R.Madych: Image recon- struction in Hilbert space -R.G.Mukhometov: A problem of in- tegral geometry for a family of rays with multiple reflec- tions -V.P.Palamodov: Inversion formulas for the three-di- mensional ray transform - Medical Imaging Techniques: V.Friedrich: Backscattered Photons - are they useful for a surface - near tomography - P.Grangeat: Mathematical frame- work of cone beam 3D reconstruction via the first derivative of the Radon transform -P.Grassin,B.Duchene,W.Tabbara: Dif- fraction tomography: some applications and extension to 3D ultrasound imaging -F.A.Gr}nbaum: Diffuse tomography: a re- fined model -R.Kress,A.Zinn: Three dimensional reconstruc- tions in inverse obstacle scattering -A.K.Louis: Mathemati- cal questions of a biomagnetic imaging problem - Inverse Problems and Optimization: Y.Censor: On variable block algebraic reconstruction techniques -P.P.Eggermont: On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems

In this volume, the collection of articles by Shepp, Helgason, Radon, and others, gives mathematicians unfamiliar with applied mathematics a rather full spectrum of models of computed tomography. Included are nice problems both relevant and of intrinsic interest suggested by each of the papers.

The Working Group 5 of the International Medical Informatics Associ ation (IMIA) dedicates its work to information systems in primary and ambulatory care. The first conference of this Working Group in Hanno ver in 1980 produced a review of the state of the art of that time and gave perspectives for future development (Rienhoff, O. and Abrams, M.E. (eds.): The Computer in the Doctor's Office, Horth Holland, Amsterdam: 1980). In the meantime, a rapid development has taken place. Therefore it seemed appropriate to hold another working conference which was con ducted in Munich, December 2-6, 1985. The goal of this working conference was to review the developments in this field and to critically evaluate the progress achieved so far. The conference addressed general principles in system development and prerequisists for their successful introduction into routine use. Furthermore, the topics of expert systems and new technologies were discussed in the context of their usefulness and usability in ambula tory care systems. As before, it became very clear that actual computer systems to sup port ambulatory and/or primary care have to meet the conditions of the health care delivery systems, into which they are to be placed.

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing. This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling expansion to higher dimensions, and applications of sampling theory to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling theory will make this an invaluable research tool as well as an excellent text for students planning further research in the field.

There exists a history of great expectations and large investments involving artificial intelligence (AI). There are also notable shortfalls and memorable disappointments. One major controversy regarding AI is just how mathematical a field it is or should be. This text includes contributions that examine the connections between AI and mathematics, demonstrating the potential for mathematical applications and exposing some of the more mathematical areas within AI. The goal is to stimulate interest in people who can contribute to the field or use its results. Included in the work by M. Newborn on the famous Deep BLue chess match. He discusses highly mathematical techniques involving graph theory, combinatorics and probability and statistics. G. Shafer offers his development of probability through probability trees with some of the results appearing here for the first time. M. Golumbic treats temporal reasoning with ties to the famous Frame Problem. His contribution involves logic, combinatorics and graph theory and leads to two chapters with logical themes. H. Kirchner explains how ordering techniques in automated reasoning systems make deduction more efficient. Constraint logic programming is discussed by C. Lassez, who shows its intimate ties to linear programming with crucial theorems going back to Fourier. V. Nalwa's work provides a brief tour of computer vision, tying it to mathematics - from combinatorics, probability and geometry to partial differential equations. All authors are gifted expositors and are current contributors to the field. The wide scope of the volume includes research problems, research tools and good motivational material for teaching.

Build the foundation necessary for the practice of CT scanning with Computed Tomography: Physical Principles, Patient Care, Clinical Applications, and Quality Control, 5th Edition. Written to meet the varied requirements of radiography students and practitioners, this two-color text provides comprehensive coverage of the physical principles of computed tomography and its clinical applications. The clear, straightforward approach is designed to improve your understanding of sectional anatomic images as they relate to computed tomography and facilitate communication between CT technologists and other medical personnel. - Chapter outlines and chapter review questions help you focus your study time and master content. - NEW! Three additional chapters reflect the latest industry CT standards in imaging: Radiation Awareness and Safety Campaigns in Computed Tomography, Patient Care Considerations, and Artificial Intelligence: An Overview of Applications in Health and Medical Imaging. - UPDATED! More than 509 photos and line drawings visually clarify key concepts. - UPDATED! The latest information keeps you up to date on advances in volume CT scanning; CT fluoroscopy; and multislice applications like 3-D imaging, CT angiography, and virtual reality imaging (endoscopy).

The book offers a comprehensive and user-oriented description of the theoretical and technical system fundamentals of computed tomography (CT) for a wide readership, from conventional single-slice acquisitions to volume acquisition with multi-slice and cone-beam spiral CT. It covers in detail all characteristic parameters relevant for image quality and all performance features significant for clinical application. Readers will thus be informed how to use a CT system to an optimum depending on the different diagnostic requirements. This includes a detailed discussion about the dose required and about dose measurements as well as how to reduce dose in CT. All considerations pay special attention to spiral CT and to new developments towards advanced multi-slice and cone-beam CT. For the third edition most of the contents have been updated and latest topics like dual source CT, dual energy CT, flat detector CT and interventional CT have been added. The enclosed CD-ROM again offers copies of all figures in the book and attractive case studies, including many examples from the most recent 64-slice acquisitions, and interactive exercises for image viewing and manipulation. This book is intended for all those who work daily, regularly or even only occasionally with CT: physicians, radiographers, engineers, technicians and physicists. A glossary describes all the important technical terms in alphabetical order. The enclosed DVD again offers attractive case studies, including many examples from the most recent 64-slice acquisitions, and interactive exercises for image viewing and manipulation. This book is intended for all those who work daily, regularly or even only occasionally with CT: physicians, radiographers, engineers, technicians and physicists. A glossary describes all the important technical terms in alphabetical order.