## Fundamentals of Computerized Tomography: Image Reconstruction from ProjectionsThis revised and updated second edition – now with two new chapters - is the only book to give a comprehensive overview of computer algorithms for image reconstruction. It covers the fundamentals of computerized tomography, including all the computational and mathematical procedures underlying data collection, image reconstruction and image display. Among the new topics covered are: spiral CT, fully 3D positron emission tomography, the linogram mode of backprojection, and state of the art 3D imaging results. It also includes two new chapters on comparative statistical evaluation of the 2D reconstruction algorithms and alternative approaches to image reconstruction. |

### What people are saying - Write a review

This book though describes about the 'fundamentals of CT', the discussion is very elaborate. But we have to appreciate, the way it is described with so many pictures to one's expectation. But for a post-graduate student in Radiology, I think, this will be too much. But for a Physicist, it is a very nice book for him to go through and later to explain the students in a simple way. Totally, a nice book for teaching others. Thank you.

### Contents

1 | |

12 Probability and Random Variables | 18 |

An Overview of the Process of CT | 27 |

23 Data Collection for CT | 30 |

24 Voxels Pixels and CT Numbers | 31 |

25 The Problem of Polychromaticity | 32 |

26 Reconstruction Algorithms | 34 |

Physical Problems Associated with Data Collection in CT | 37 |

87 Why So Popular? | 157 |

Other Transform Methods for Parallel Beams | 159 |

92 The Fourier Method of Reconstruction | 161 |

93 Linograms | 166 |

94 RhoFiltered Layergram | 173 |

Filtered Backprojection for Divergent Beams | 177 |

102 Choice of the Window Function | 181 |

103 Point Response Function | 182 |

32 Beam Hardening | 42 |

33 Other Sources of Error | 44 |

34 Scanning Modes | 47 |

Computer Simulation of Data Collection in CT | 53 |

42 Creation of a Phantom | 54 |

43 A PiecewiseHomogeneous Head Phantom | 56 |

44 Head Phantom with a Large Tumor and Local Inhomogeneities | 59 |

45 Creation of the Ray Sums | 60 |

46 Fast Calculation of a Ray Sum for a Digitized Picture | 63 |

Data Collection and Reconstruction of the Head Phantom | 66 |

52 TaskOriented Comparison of Algorithm Performance | 69 |

53 An Illustration Using Selective Smoothing | 73 |

54 Reconstruction from Perfect Data | 78 |

55 Effects of Photons Statistics | 83 |

56 Effect of Beam Hardening | 86 |

57 The Effects of Detector Width and Scatter | 91 |

58 Simulation of Different Scanning Modes | 95 |

Basic Concepts of Reconstruction Algorithms | 100 |

62 Transform Methods | 106 |

63 Series Expansion Methods | 108 |

64 Optimization Criteria | 111 |

65 Blob Basis Functions | 119 |

66 Computational Efficiency | 122 |

Backprojection | 125 |

72 Implementation of the Backprojection Operator | 127 |

73 Discrete Backprojection | 131 |

Filtered Backprojection for Parallel Beams | 135 |

82 Derivation of the FBP Method | 139 |

83 Implementation of the FBP Method | 140 |

84 Fourier Transforms | 143 |

85 Sampling and Interpolation | 146 |

86 The Choice of Convolving and Interpolating Functions | 147 |

104 Noise Reconstruction | 186 |

105 Comparison of Algorithms Based on Reconstructions | 188 |

Algebraic Reconstruction Techniques | 193 |

112 Relaxation Methods for Solving Systems of Inequalities and Equalities | 196 |

113 Additive ART | 201 |

114 Tricks | 205 |

115 Efficacy of ART | 210 |

Quadratic Optimization Methods | 217 |

122 Richardsons Method for Solving Systems of Equations | 221 |

123 Smoothing Matrices | 224 |

124 Implementation of Richardsons Methods for Image Reconstruction | 226 |

125 A Demonstration of Quadratic Optimization | 227 |

Truly ThreeDimensional Reconstruction | 234 |

131 ThreeDimensional Series Expansion | 236 |

132 Dynamically Changing 3D Phantoms and Their Projections | 237 |

133 ThreeDimensional Reconstructions of the Dynamic Phantom | 240 |

ThreeDimensional Display of Organs | 243 |

142 Boundary Detection | 246 |

143 Hidden Surface Removal | 251 |

144 Shading | 253 |

Mathematical Background | 259 |

152 The Line Integral of the Relative Linear Attenuation | 260 |

153 The Radon Inversion Formula | 261 |

154 A Picture Is Not Uniquely Determined by a Finite Number of Its Views | 265 |

155 Analysis of the Photon Statistics | 267 |

156 The Integral Expression for Polychromatic Ray Sums | 269 |

157 Proof of the Regularization Theorem | 270 |

158 Convergence of the Relaxation Method for Inequalities | 273 |

277 | |

292 | |

### Other editions - View all

Fundamentals of Computerized Tomography: Image Reconstruction from Projections Gabor T. Herman No preview available - 2009 |

Fundamentals of Computerized Tomography: Image Reconstruction from Projections Gabor T. Herman No preview available - 2012 |