| Preface |
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xvii | |
| Notation |
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xxi | |
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Introduction to Tomography |
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1 | (20) |
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1 | (1) |
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2 | (5) |
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Localization in space and time |
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7 | (2) |
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9 | (3) |
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12 | (5) |
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17 | (4) |
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PART
1. IMAGE RECONSTRUCTION |
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21 | (96) |
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23 | (40) |
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23 | (2) |
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2D Radon transform in parallel-beam geometry |
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25 | (7) |
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Definition and concept of sinogram |
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25 | (1) |
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Fourier slice theorem and data sufficiency condition |
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26 | (1) |
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Inversion by filtered backprojection |
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27 | (1) |
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28 | (3) |
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Frequency-distance principle |
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31 | (1) |
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2D Radon transform in fan-beam geometry |
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32 | (5) |
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32 | (1) |
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Rebinning to parallel data |
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33 | (1) |
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Reconstruction by filtered backprojection |
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33 | (1) |
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34 | (1) |
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3D helical tomography in fan-beam geometry with a single line detector |
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35 | (2) |
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3D X-ray transform in parallel-beam geometry |
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37 | (3) |
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37 | (1) |
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Fourier slice theorem and data sufficiency conditions |
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38 | (1) |
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Inversion by filtered backprojection |
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39 | (1) |
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40 | (2) |
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40 | (1) |
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41 | (1) |
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Inversion by filtered backprojection |
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41 | (1) |
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3D positron emission tomography |
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42 | (4) |
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42 | (1) |
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Approximate reconstruction by rebinning to transverse slices |
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42 | (3) |
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Direct reconstruction by filtered backprojection |
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45 | (1) |
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X-ray tomography in cone-beam geometry |
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46 | (8) |
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46 | (1) |
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Connection to the derivative of the 3D Radon transform and data sufficiency condition |
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46 | (3) |
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Approximate inversion by rebinning to transverse slices |
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49 | (1) |
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Approximate inversion by filtered backprojection |
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50 | (2) |
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Inversion by rebinning in Radon space |
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52 | (1) |
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Katsevich algorithm for helical cone-beam reconstruction |
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53 | (1) |
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54 | (4) |
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54 | (1) |
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2D dynamic Radon transform |
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54 | (1) |
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Dynamic X-ray transform in divergent geometry |
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55 | (1) |
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55 | (3) |
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58 | (5) |
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Sampling Conditions in Tomography |
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63 | (26) |
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Sampling of functions in Rn |
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63 | (8) |
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Periodic functions, integrable functions, Fourier transforms |
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63 | (2) |
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Poisson summation formula and sampling of bandlimited functions |
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65 | (1) |
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Sampling of essentially bandlimited functions |
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66 | (2) |
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68 | (2) |
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Generalization to periodic functions in their first variables |
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70 | (1) |
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Sampling of the 2D Radon transform |
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71 | (8) |
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Essential support of the 2D Radon transform |
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71 | (2) |
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Sampling conditions and efficient sampling |
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73 | (1) |
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74 | (1) |
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74 | (2) |
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Generalized, rotation invariant Radon transform |
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76 | (1) |
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Exponential and attenuated Radon transform |
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77 | (2) |
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Sampling in 3D tomography |
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79 | (6) |
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79 | (1) |
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Sampling of the X-ray transform |
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80 | (4) |
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Numerical results on the sampling of the cone-beam transform |
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84 | (1) |
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85 | (4) |
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89 | (28) |
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89 | (1) |
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90 | (2) |
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92 | (7) |
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Case of overdetermination by the data |
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92 | (1) |
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Algebraic methods based on quadratic minimization |
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92 | (1) |
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93 | (3) |
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Case of underdetermination by the data |
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96 | (1) |
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Algebraic methods based on constraint optimization |
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96 | (1) |
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97 | (2) |
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99 | (11) |
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Case of overdetermination by the data |
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99 | (1) |
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Bayesian statistical methods |
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99 | (1) |
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100 | (1) |
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Markov fields and Gibbs distributions |
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100 | (2) |
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102 | (1) |
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Choice of hyperparameters |
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103 | (2) |
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MAP reconstruction algorithms |
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105 | (1) |
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105 | (1) |
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105 | (1) |
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Semi-quadratic regularization |
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106 | (1) |
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Regularization algorithm ARTUR |
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106 | (1) |
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Regularization algorithm MOISE |
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107 | (1) |
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Case of underdetermination by the data |
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107 | (1) |
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107 | (2) |
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109 | (1) |
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Example of tomographic reconstruction |
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110 | (1) |
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Discussion and conclusion |
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110 | (2) |
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112 | (5) |
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117 | (98) |
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119 | (22) |
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119 | (1) |
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Projection tomography in electron microscopy |
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120 | (1) |
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Tomography by optical sectioning |
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121 | (8) |
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Confocal laser scanning microscopy (CLSM) |
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122 | (1) |
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Principle of confocal microscopy |
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122 | (1) |
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123 | (3) |
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126 | (2) |
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Fluorochromes employed in confocal microscopy |
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128 | (1) |
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3D data processing, reconstruction and analysis |
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129 | (9) |
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129 | (1) |
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130 | (1) |
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130 | (2) |
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132 | (1) |
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132 | (3) |
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Microscopy by multiphoton absorption |
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135 | (3) |
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138 | (3) |
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141 | (56) |
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141 | (1) |
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Interaction of light with matter |
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142 | (8) |
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143 | (2) |
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145 | (1) |
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146 | (1) |
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146 | (1) |
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146 | (4) |
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Propagation of photons in diffuse media |
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150 | (14) |
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151 | (5) |
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Mixed coherent/incoherent propagation |
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156 | (1) |
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157 | (1) |
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Radiative transfer theory |
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158 | (6) |
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Optical tomography methods |
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164 | (17) |
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Optical coherence tomography |
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166 | (1) |
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166 | (3) |
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169 | (1) |
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Principle of the reconstruction of the object in diffraction tomography |
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170 | (4) |
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174 | (2) |
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Optical coherence tomography |
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176 | (1) |
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Role of the coherence length |
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177 | (1) |
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The principle of coherent detection |
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178 | (1) |
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178 | (2) |
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Coherence tomography in the temporal domain |
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180 | (1) |
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Coherence tomography in the spectral domain |
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181 | (1) |
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Optical tomography in highly diffuse media |
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181 | (9) |
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Direct model, inverse model |
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182 | (2) |
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184 | (1) |
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184 | (1) |
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184 | (1) |
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185 | (1) |
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186 | (1) |
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186 | (1) |
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Reconstruction by inverse projection |
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187 | (1) |
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187 | (2) |
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189 | (1) |
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190 | (7) |
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197 | (18) |
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197 | (1) |
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197 | (5) |
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197 | (4) |
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Advantages of synchrotron radiation for tomography |
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201 | (1) |
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202 | (4) |
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202 | (2) |
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ESRF system and applications |
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204 | (2) |
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Microtomography using synchrotron radiation |
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206 | (4) |
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206 | (1) |
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ESRF system and applications |
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207 | (3) |
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210 | (1) |
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Phase contrast and holographic tomography |
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210 | (1) |
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Tomography by refraction, diffraction, diffusion and fluorescence |
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211 | (1) |
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211 | (1) |
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212 | (3) |
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PART
3. INDUSTRIAL TOMOGRAPHY |
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215 | (42) |
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X-ray Tomography in Industrial Non-destructive Testing |
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217 | (22) |
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217 | (1) |
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Physics of the measurement |
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218 | (1) |
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219 | (1) |
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220 | (3) |
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Reconstruction algorithms and artifacts |
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223 | (1) |
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223 | (1) |
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223 | (1) |
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223 | (1) |
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224 | (11) |
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224 | (1) |
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225 | (1) |
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225 | (1) |
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CAD models in tomography: reverse engineering and simulation |
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226 | (1) |
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227 | (1) |
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227 | (1) |
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228 | (2) |
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230 | (1) |
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230 | (2) |
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232 | (1) |
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233 | (2) |
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235 | (1) |
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236 | (3) |
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Industrial Applications of Emission Tomography for Flow Visualization |
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239 | (18) |
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Industrial applications of emission tomography |
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239 | (3) |
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239 | (1) |
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240 | (1) |
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240 | (2) |
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242 | (5) |
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242 | (2) |
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Flow in a pipe - analysis of a junction |
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244 | (3) |
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Physical model of data acquisition |
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247 | (5) |
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247 | (1) |
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Principle of the Monte Carlo simulation |
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248 | (1) |
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Calculation of projection matrices |
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249 | (1) |
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Estimation of projection profiles |
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249 | (2) |
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Estimation of the projection matrix |
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251 | (1) |
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Definition and characterization of a system |
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252 | (3) |
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Characteristic system parameters |
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252 | (2) |
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Characterization of images reconstructed with the EM algorithm |
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254 | (1) |
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254 | (1) |
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255 | (1) |
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255 | (2) |
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PART
4. MORPHOLOGICAL MEDICAL TOMOGRAPHY |
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257 | (70) |
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259 | (28) |
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259 | (6) |
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259 | (1) |
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260 | (1) |
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Scanners with continuous rotation |
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261 | (2) |
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263 | (1) |
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Medical applications of CT |
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264 | (1) |
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Physics of helical tomography |
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265 | (7) |
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Projection acquisition system |
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265 | (1) |
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Mechanics for continuous rotation |
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266 | (1) |
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X-ray tubes with large thermal capacity |
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266 | (1) |
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X-ray detectors with high dynamics, efficiency, and speed |
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266 | (1) |
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267 | (1) |
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Reconstruction algorithms |
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267 | (1) |
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267 | (1) |
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268 | (1) |
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269 | (1) |
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270 | (1) |
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270 | (1) |
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Longitudinal spatial resolution |
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270 | (1) |
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270 | (1) |
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271 | (1) |
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271 | (1) |
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Applications of volume CT |
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272 | (7) |
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Role of visualization of axial slices |
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272 | (1) |
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Role of 2D and 3D postprocessing |
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272 | (1) |
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272 | (1) |
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273 | (3) |
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276 | (1) |
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277 | (2) |
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279 | (1) |
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279 | (1) |
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279 | (1) |
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280 | (7) |
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Interventional X-ray Volume Tomography |
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287 | (20) |
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287 | (3) |
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287 | (1) |
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288 | (1) |
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Positioning with respect to computed tomography |
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289 | (1) |
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Example of 3D angiography |
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290 | (7) |
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Principles of projection acquisition |
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291 | (1) |
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291 | (1) |
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291 | (4) |
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295 | (1) |
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Other reconstruction methods in 3D radiology |
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296 | (1) |
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297 | (1) |
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297 | (5) |
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High contrast applications |
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298 | (1) |
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Soft tissue contrast applications |
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299 | (1) |
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300 | (2) |
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302 | (1) |
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303 | (4) |
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Magnetic Resonance Imaging |
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307 | (20) |
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307 | (1) |
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Nuclear paramagnetism and its measurement |
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308 | (4) |
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308 | (1) |
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Nuclear magnetic relaxation and Larmor precession |
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308 | (1) |
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309 | (2) |
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311 | (1) |
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Spatial encoding of the signal and image reconstruction |
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312 | (6) |
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Information content of the signal's phase |
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312 | (2) |
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Signal sampling along k-space trajectories and use of a 2D model |
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314 | (1) |
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Cartesian k-space sampling |
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314 | (2) |
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Non-Cartesian k-space sampling |
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316 | (2) |
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Contrast factors and examples of applications |
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318 | (5) |
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Density of nuclei and magnetization |
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318 | (1) |
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Relaxation times and discrimination between soft tissues |
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318 | (2) |
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320 | (1) |
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Relevance of magnetization transfer techniques |
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320 | (1) |
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321 | (1) |
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Diffusion and perfusion effects |
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322 | (1) |
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323 | (1) |
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323 | (4) |
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PART
5. FUNCTIONAL MEDICAL TOMOGRAPHY |
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327 | (84) |
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Single Photon Emission Computed Tomography |
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329 | (22) |
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329 | (1) |
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329 | (1) |
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Functional versus anatomical imaging |
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329 | (1) |
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330 | (1) |
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330 | (1) |
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Radioactive gamma markers |
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331 | (1) |
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331 | (5) |
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General principle of the gamma camera |
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331 | (1) |
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Special features of single photon detection: collimator and spectrometry |
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332 | (1) |
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Principle characteristics of the gamma camera |
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333 | (1) |
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Principle of projection acquisition |
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334 | (1) |
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Transmission measurement system |
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335 | (1) |
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336 | (7) |
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336 | (1) |
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Reconstruction algorithms |
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337 | (1) |
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Tomographic reconstruction problem in SPECT |
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337 | (1) |
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Analytical reconstruction in SPECT |
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338 | (1) |
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Algebraic reconstruction in SPECT |
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338 | (1) |
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Specific problems of single photon detection |
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339 | (1) |
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340 | (1) |
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340 | (1) |
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341 | (1) |
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Variation of the spatial resolution with depth |
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342 | (1) |
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Example of myocardial SPECT |
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343 | (3) |
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343 | (1) |
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Radiopharmaceuticals, injection and acquisition protocols |
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344 | (1) |
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Reconstruction and interpretation criteria |
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344 | (1) |
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Importance of the accuracy of the projection model |
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345 | (1) |
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346 | (1) |
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346 | (2) |
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348 | (3) |
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Positron Emission Tomography |
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351 | (26) |
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351 | (2) |
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351 | (1) |
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PET versus other functional imaging techniques |
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351 | (2) |
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Functional versus anatomical imaging |
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353 | (1) |
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353 | (10) |
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353 | (1) |
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353 | (1) |
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Positron emitting markers |
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354 | (1) |
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Physical principle of PET |
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354 | (1) |
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354 | (1) |
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Principle of coincidence detection |
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355 | (1) |
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Type of detected coincidences |
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355 | (1) |
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Detection systems employed in PET |
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356 | (1) |
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356 | (1) |
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357 | (1) |
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Physical characteristics of scanners |
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358 | (1) |
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358 | (1) |
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Two-dimensional (2D) acquisition |
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358 | (2) |
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Three-dimensional (3D) acquisition |
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360 | (1) |
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3D data organization for a multiline scanner |
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361 | (1) |
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LOR and list mode acquisition |
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361 | (1) |
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Acquisition with time-of-flight measurement |
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362 | (1) |
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Transmission scan acquisition |
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362 | (1) |
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363 | (7) |
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364 | (1) |
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Reconstruction of corrected data |
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365 | (1) |
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366 | (1) |
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Measurement of glucose metabolism |
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367 | (1) |
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368 | (1) |
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369 | (1) |
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Research and clinical applications of PET |
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370 | (3) |
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Clinical applications of PET: whole-body measurements of glucose metabolism in oncology |
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370 | (1) |
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370 | (1) |
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Acquisition and reconstruction protocol |
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370 | (1) |
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Image interpretation: sensitivity and specificity of this medical imaging modality |
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371 | (1) |
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Clinical research applications: study of dopaminergic transmission |
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372 | (1) |
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Dopaminergic transmission system |
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372 | (1) |
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372 | (1) |
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372 | (1) |
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Example of use: study of neurodegenerative diseases that affect the basal ganglia |
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373 | (1) |
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373 | (1) |
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374 | (3) |
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Functional Magnetic Resonance Imaging |
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|
377 | (16) |
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377 | (1) |
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Functional MRI of cerebrovascular responses |
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|
378 | (2) |
|
|
|
380 | (3) |
|
|
|
380 | (1) |
|
|
|
381 | (1) |
|
``Intermediate'' conditions |
|
|
382 | (1) |
|
``Motional narrowing'' conditions |
|
|
382 | (1) |
|
|
|
383 | (1) |
|
|
|
383 | (6) |
|
|
|
384 | (1) |
|
|
|
384 | (3) |
|
|
|
387 | (2) |
|
|
|
389 | (4) |
|
Tomography of Electrical Cerebral Activity in Magneto- and Electro-encephalography |
|
|
393 | (18) |
|
|
|
|
|
393 | (1) |
|
Principles of MEG and EEG |
|
|
394 | (4) |
|
|
|
394 | (1) |
|
|
|
395 | (1) |
|
|
|
395 | (2) |
|
|
|
397 | (1) |
|
Imaging of electrical activity of the brain based on MEG and EEG signals |
|
|
398 | (9) |
|
Difficulties of reconstruction |
|
|
398 | (1) |
|
Direct problem and different field calculation methods |
|
|
399 | (3) |
|
|
|
402 | (1) |
|
Parametric or ``dipolar'' methods |
|
|
403 | (2) |
|
Tomographic or ``distributed'' methods |
|
|
405 | (2) |
|
|
|
407 | (1) |
|
|
|
408 | (3) |
| List of Authors |
|
411 | (6) |
| Index |
|
417 | |
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