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Mathematical Aspects of Computerized Tomography

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Cover of 'Mathematical Aspects of Computerized Tomography'

Table of Contents

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    Book Overview
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    Chapter 1 Early Tomography and Related Topics
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    Chapter 2 Finite Versions of the Radon-Transform Based on Finite Geometric Structures
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    Chapter 3 Stability of Solutions to Linear Operator Equations of the First and Second Kinds Under Perturbation of the Operator with Rank Change
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    Chapter 4 The Problem of Reconstructing Objects from Projections as an Inverse Problem in Scattering Theory of the Linear Transport Operator
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    Chapter 5 On the Problem of Well-Posedness for the Radon Transform
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    Chapter 6 The Identification Problem in Emission Computed Tomography
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    Chapter 7 Generalized Radon Transformations
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    Chapter 8 The Radon Transform in ℝ 2 . The Distributions Used as a Tool for its Inversion in Circular Decomposition and Elimination of an Additive Noise. Systematic Tables of Transforms
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    Chapter 9 Stability and Consistency for the Divergent Beam X-Ray Transform
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    Chapter 10 Reconstruction with Arbitrary Directions: Dimensions Two and Three
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    Chapter 11 Approximation of the Radon Transform from Samples in Limited Range
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    Chapter 12 Redundancy in 360° Direct Fan-Beam Reconstruction
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    Chapter 13 Intervals in Linear and Nonlinear Problems of Image Reconstruction
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    Chapter 14 Continuous and Semicontinuous Analogues of Iterative Methods of Cimmino and Kaczmarz with Applications to the Inverse Radon Transform
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    Chapter 15 A Minimax Performance Measure for Computed Tomography
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    Chapter 16 A New Approach to the Numerical Evaluation of the Inverse Radon Transform with Discrete, Noisy Data
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    Chapter 17 Surfaces of Organs in Discrete Three-Dimensional Space
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    Chapter 18 On Two Approaches to 3D Reconstruction in NMR Zeugmatography
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    Chapter 19 Resolution Improvement to C.T.Systems Using Aperture Function Correction
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    Chapter 20 Nonlinearity and Inhomogenity Effects in Computerized Tomography Due to the Exponential Attenuation of Radiation
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    Chapter 21 Nonlinear Image Reconstruction from Projections of Ultrasonic Travel Times and Electric Current Densities
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    Chapter 22 Sampling and Discretization Problems in X-ray-CT
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Title
Mathematical Aspects of Computerized Tomography
Published by
Springer Berlin Heidelberg, March 2013
DOI 10.1007/978-3-642-93157-4
ISBNs
978-3-54-010277-9, 978-3-64-293157-4
Editors

Herman, G. T., Natterer, Frank

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