Mathematical Aspects of Computerized Tomography: Proceedings, Oberwolfach, February 10-16, 1980

ISBN-13: 9783540102779 / Angielski / Miękka / 1981 / 310 str.

G. T. Herman; F. Natterer

Opis

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.

Spis treści

Early Tomography and Related Topics.- Mathematical Analysis.- Finite Versions of the Radon-Transform Based on Finite Geometric Structures.- Stability of Solutions to Linear Operator Equations of the First and Second Kinds Under Perturbation of the Operator with Rank Change.- The Problem of Reconstructing Objects from Projections as an Inverse Problem in Scattering Theory of the Linear Transport Operator.- On the Problem of Well-Posedness for the Radon Transform.- The Identification Problem in Emission Computed Tomography.- Generalized Radon Transformations.- The Radon Transform in ?2. The Distributions Used as a Tool for its Inversion in Circular Decomposition and Elimination of an Additive Noise. Systematic Tables of Transforms -.- Stability and Consistency for the Divergent Beam X-Ray Transform.- Reconstruction from Limited Data.- Reconstruction with Arbitrary Directions: Dimensions Two and Three.- Approximation of the Radon Transform from Samples in Limited Range.- Redundancy IN 360° Direct Fan-Beam Reconstruction.- Regularization and Optimization.- Intervals in Linear and Nonlinear Problems of Image Reconstruction.- Continuous and Semicontinuous Analogues of Iterative Methods of Cimmino and Kaczmarz with Applications to the Inverse Radon Transform.- A Minimax Performance Measure for Computed Tomography.- A New Approach to the Numerical Evaluation Of The Inverse Radon Transform with Discrete, Noisy Data.- Application Oriented Topics.- Surfaces of Organs in Discrete Three-Dimensional Space.- On Two Approaches to 3D Reconstruction in Nmr Zeugmatography.- Resolution Improvement to C.T.Systems Using Aperture Function Correction.- Nonlinearity and Inhomogenity Effects in Computerized Tomography Due to the Exponential Attenuation of Radiation.- Nonlinear Image Reconstruction from Projections of Ultrasonic Travel Times and Electric Current Densities.- Sampling and Discretization Problems In X-Ray-CT.