Page 231

Index

A

acoustical holography 123

acoustical index of refraction 124

adaptive current tomograph (ACT) 145

aliasing 62

amplifier design 70

analytical inversion 117

anatomical priors 193

angiography 52

imaging techniques for 62

angioplasty 171

anisotropic diffusion 82

applied potential tomography (APT) system 145

artifacts 28, 60

motion-related 29, 66

patient-related 29

physics-related 28

ring-shaped 29

system-related 29

attenuation 24, 30, 91, 97, 98, 99, 126, 159, 202

coefficients 24, 91, 97-99

compensation 99

distribution 159, 202

distribution, non-uniform 91, 99

distribution, uniform 99

linear 24

SPECT 91, 97, 98

three-dimensional correction, 118

ultrasound 126

avalanche photodiodes 109

B

backprojection method 209

backpropagation method 127

Bayesian method 56, 59, 61, 204, 223, 224

beam forming 122, 124

beam hardening 25, 28, 30, 200

artifacts 25

beam propagation 123

boundary-element method (BEM) 136, 137, 150

biopsy 169, 173

Biot-Savart law 149, 213

Bloch equation 38, 209

blood flow 37, 62, 67, 106

imaging of 37

blood oxygen level dependent (BOLD) effect 69

Born approximation 205

C

cardiac imaging 19, 91, 99

cardiac strain 67

Cauchy problem 136, 214

chemical shift imaging 75

chest radiography 14, 16, 18

cluster analysis 189

coil designs 54, 79

partial-volume 50

superconducting 79



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Page 231 Index A acoustical holography 123 acoustical index of refraction 124 adaptive current tomograph (ACT) 145 aliasing 62 amplifier design 70 analytical inversion 117 anatomical priors 193 angiography 52 imaging techniques for 62 angioplasty 171 anisotropic diffusion 82 applied potential tomography (APT) system 145 artifacts 28, 60 motion-related 29, 66 patient-related 29 physics-related 28 ring-shaped 29 system-related 29 attenuation 24, 30, 91, 97, 98, 99, 126, 159, 202 coefficients 24, 91, 97-99 compensation 99 distribution 159, 202 distribution, non-uniform 91, 99 distribution, uniform 99 linear 24 SPECT 91, 97, 98 three-dimensional correction, 118 ultrasound 126 avalanche photodiodes 109 B backprojection method 209 backpropagation method 127 Bayesian method 56, 59, 61, 204, 223, 224 beam forming 122, 124 beam hardening 25, 28, 30, 200 artifacts 25 beam propagation 123 boundary-element method (BEM) 136, 137, 150 biopsy 169, 173 Biot-Savart law 149, 213 Bloch equation 38, 209 blood flow 37, 62, 67, 106 imaging of 37 blood oxygen level dependent (BOLD) effect 69 Born approximation 205 C cardiac imaging 19, 91, 99 cardiac strain 67 Cauchy problem 136, 214 chemical shift imaging 75 chest radiography 14, 16, 18 cluster analysis 189 coil designs 54, 79 partial-volume 50 superconducting 79

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Page 232 coil designs (continued) surface gradient coils 50 whole-body gradient coils 49 whole-volume coils 50 collimator designs 93, 94, 101, 102 astigmatic 101 cone-beam 94, 101 converging-hole, 94 fan-beam 94 parallel-hole 94 variable focal 101 see also RF coils, gradient coils collimator-detector response 98 collimator-detector system 100 Compton scattering 91, 96, 108, 118 computational anatomy 191 computed tomography (CT) 1, 14, 23, 157, 159, 160, 168 CT angiography 33, 34 high-speed 30 spiral CT 23, 31, 33, 169 computer-assisted visualization 168 conductivity distribution 144 cone beam errors 33 conjugate gradient algorithm 99 contrast agents 162 contrast resolution 23 contrast-to-noise ratio 79 convergence 204 convolution kernels 31 convolution methods 98 cryosurgery 177, 178, 194 D data acquisition 33, 34, 41, 45, 47, 56-59, 62, 63, 70, 94, 101, 112, 116, 125, 134, 157, 158, 175, 187, 193 for optical methods 158 systems 27 three-dimensional 114, 116 data correction 27, 112 data display 33, 63 multi-dimensional 187 three-dimensional 31, 33, 74, 129 data fitting 191, 193 data fusion 188 data interpolation 31 data reduction 33, 187, 193 data sampling 117 data visualization 188 detector systems arrays 33, 148 efficiency 108 elements 27, 108 noise in 153 ring-based 28 scintillators 27, 92 SPECT 95 transducer development 122 see also scintillation cameras, scintillation crystals dielectric constant, changes in 143 diffraction integral 123 diffraction tomography 127, 206 diffusion 80-82 anisotropic 82 coefficients 65 measurements 66 diffusion MRI 49, 66 application to strokes 81 diffusion tensor imaging (DTI) 81 digital subtraction angiography (DSA) 13 discrete Fourier transform 40 display 31, 33, 68, 74, 81, 125, 129 three-dimensional 31, 33, 74, 129

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Page 233 Doppler shift 211 Doppler tomography 212, 226 dynamic imaging 4, 37, 56, 93 E echo-planar imaging (EPI) 49, 50, 53, 56, 60, 63, 66, 68-70, 74, 81, 171 eddy currents 50, 60, 73, 74, 81 in MRI 50 edge detection 189 elastic warping 192 electrical impedance tomography (EIT) 143, 209, 216 electronics for 144 inversion algorithms for 144 electrical source imaging (ESI) 214 electrocardiography (ECG) 133, 134 electroencephalography (EEG) 3, 133 electron beam systems 32-34 emission CT 202, 203 endocardial potentials 135 endoscopy 167, 170 energy resolution 117, 119 expectation maximization algorithm 99, 113 F fan beam systems 25, 28, 29 reconstruction algorithm for 25 fast Fourier transform (FFT) 56, 57, 60, 61, 222 Fermi motion 110 field inhomogeneities 58 film subtraction angiography 13 filtered backprojection algorithm 33, 115, 118, 119, 200, 204 three-dimensional 116, 117 filtered backprojection of filtered projection 98 finite-element method (FEM) 46, 74, 123, 136, 137, 150 fitting algorithm 193 focused ultrasound (FUS) 4, 179, 180 forward models 153 forward problem 136, 215 Fourier optics 124 Fourier projection theorem 98, 113 Fourier reconstruction 117 Fourier space interpolation 211 Fourier transform 40, 52, 58, 117, 206, 210, 211, 222 FFT 56, 57, 60, 61, 222 functional imaging 3 functional magnetic resonance imaging (fMRI) 1, 68, 70, 72-74, 148 fuzzy logic 189 G Gauss-Seidel algorithm 99 Gelfand-Levitan procedure 217 Gibbs-Markov random field 204 Gibbs ringing 57, 58 global thresholding 189 gradient coils 49, 51, 70, 72 for MRI 49 local 50, 51 surface 78 whole-body 49 gradient descent method 52 H half-value layer 91 heart arrhythmia 135 heat surgery 177 Helmholtz equation 224 high-temperature superconductor 37 magnets 42 histogramming 189

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Page 234 Holder stability 218 holography 21 Hounsfield numbers 30 hyperpolarized gases 78 I ill-posedness 59, 115, 136, 144, 160, 209, 214, 217, 218 image combination, image fusion 47, 193 image contrast 66 image-guided therapy 168 image processing 187, 188, 193 image processing methods 64, 189, 190, 194 cluster analysis 189 edge detection 189 enhancement 187 filtering 56 global thresholding 189 histogramming 189 region growing 190 registration 174, 175, 189, 191, 193, 195 segmentation 77, 188-191, 194 shape analysis 189 statistical edge finding 189 surface rendering 194 thresholding 190 volume rendering 194 see also signal processing image reconstruction 25, 31, 33, 37, 48, 56, 60, 61, 91, 99, 106, 113, 116, 135, 154 see also reconstruction immobilization during intervention 174 impedance tomography (see electrical impedance tomography) index of refraction, acoustical 124 instability of instruments 71 mathematical 209, 214, 216, 217 integral geometry 211 interpolation 48 in Fourier space 211 interventional MRI 4, 66 interventional radiology 168 inverse problem 113, 114, 135-137, 148, 202, 205, 206, 208, 209, 214-216, 224 inversion algorithms for EIT 144 inversion problem 158, 160 iterative reconstruction algorithms 98-101, 151 conjugate gradient 99 expectation maximization 99, 113 Gauss-Seidel 99 K k-space coverage 56 keyhole imaging 60 Klein-Nishina formula 118 L Lagrange multipliers 52 LANDSAT 190 laser optical tomography 157, 160 layer stripping 209 Levenberg-Marquardt iterative method 216, 221 light tomography 208 limited-angle reconstruction, SPECT 101 linear attenuation coefficient 24 local gradient coils 50, 51 local RF coils 50 logarithmic stability 218 magnetic field gradients 70

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Page 235 magnetic resonance (MR) 37 magnetic resonance angiography (MRA) 74, 194 magnetic resonance imaging (MRI) 1, 3, 5, 14, 37, 38, 159, 167, 169-171, 176, 190, 209-211 fast data acquisition 175 flow imaging 65 intervention and 66, 172 magnetic field for 41 magnets for 42, 175 microscopy 80 pulsed-field 44 magnetic resonance spectroscopy (MRS) 75 magnetic source imaging (MSI) 147-149, 152, 213, 214 sensors for 148 magnetocardiography (MCG) 147 magnetoencephalography (MEG) 147 mammography 14, 15 maximum a posteriori (MAP) method 99 maximum entropy method 61, 99, 100, 193, 220 maximum likelihood method 99, 100, 204 measurement of electrical conductivity 144 measurement of oxygen 67 Metz filter 100 microscopic imaging 78 microscopy 1 minimally invasive surgery 168 minimum mean squares error 100 Monte Carlo methods 52 motion detection 189 movement during data acquisition 29, 66, 193 multi-dimensional data 187 multiple coils 47, 48, 54 multiple receivers 48 N neural networks 61, 189 Newton's method 209, 216 noise 28, 70, 91, 99, 117, 118, 136, 153, 154, 160 detector 153 patient-based 46 physiological 73 quantum 28 nuclear magnetic resonance (NMR) imaging—see magnetic resonance imaging nuclear medicine imaging 89, 90, 95 objective function 138 optical tomography 158, 161, 207, 208, 216 data collection for 158 paramagnetic contrast agents 78 parametric estimation techniques 59 patient management 167 perturbation theory 127 phase aberration 124 phase-contrast MR imaging 62 phase errors 57 phase mapping methods 63, 64, 68 phased array system 123 photomultiplier tubes 90, 108 photon attenuation and scatter 97 physics-related artifacts 28 positron emission tomography (PET) 3, 105-114, 117, 119, 148, 159, 160, 203

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Page 236 PET (continued) data corrections 112 detectors 109, 117 detector systems 108, 112 efficiency 108 image reconstruction 113 scintillators for 109 system electronics 111 precession frequency 39 principal component analysis (PCA), combination by 47, 48 priors (prior information) 154, 204 anatomical 193 use of 153, 154 projection on convex subsets (POCS) 223 pulsatile flow 63 pulse-echo techniques 126 pulse sequences 171 pulsed-field MRI 44 Q quantum efficiency 27 R radiopharmaceuticals 90, 91 Radon inversion formula 200 Radon transform 200, 211, 212 attenuated 97 inverse 98 real-time imaging 168 reconstruction 26, 28, 56, 94, 96, 112, 135, 152, 158 reconstruction methods 33, 34, 60, 127 backpropagation method 127 limited-angle reconstruction 101 maximum a posteriori (MAP) 99 maximum entropy 61, 99, 193, 220 maximum likelihood 99, 204 PET 113 three-dimensional 119 see also image reconstruction region growing 190 regularization methods 138, 214, 215, 217, 218, 220-222 Tikhonov-Phillips 221 reprojection techniques 194 resolution 60, 65, 78-80, 90, 91, 93-96, 109, 110, 116, 121, 125-127, 144, 150, 152, 161, 206, 221 EIT 144 energy 117, 119 ESI 135 MSI 152 PET 110 spatial 23, 31, 33, 49, 51, 56, 58, 59, 90, 92, 94-96, 110, 135, 144, 152 SPECT 92, 94-96 temporal 49, 152 restoration filter 100 RF coils 41, 45 design 45, 51, 53 efficiency 52 local 50 partial-volume 50 ring detector based systems 26, 28 robot-assisted surgery 168 Rytov approximation 127 S sampling 23, 33, 60, 124, 221, 222 Fourier space 222 three-dimensional 221 scanner aperture 117 scan times 23 scattering 126, 159, 201

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Page 237 scattering (continued) correction/compensation 20, 100, 117, 118 response function 100 scintillation cameras 95, 102 scintillation crystals 108 see also detector elements segmentation 77, 188-191, 194 spectral techniques 190 shape analysis 189 signal processing 62, 80, 124, 125 see also image processing signal-to-noise ratio (SNR) 43, 44, 46, 51, 56, 60-63, 79, 116, 117, 152, 193 simplex method 52, 193 simulated annealing 52, 193 single photon emission computed tomography (SPECT) 7, 90-94, 96-102, 148, 159, 160, 203 brain 93 converging-beam 102 dynamic 93 heart 91, 99 instrumentation 90-92 sensitivity 96 singular value decomposition 193 spatial resolution 23, 31, 33, 49, 51, 56, 58, 59, 90, 92, 94-96, 110, 135, 144, 152 speckle 124 SPECT detectors 95 cadmium zinc telluride 95 germanium 95 multi-detector systems 92, 93 semiconductor 95 silicon 95 SPECT image reconstruction 91, 96-99 iterative methods 99 limited-angle 101 SPECT system design—see SPECT instrumentation 93 spectroscopic imaging 75, 76 spiral CT 23, 31, 33, 169 spiral scan methods 63 SQUIDs (superconducting quantum interference devices) 147, 148, 150, 153 stability, magnetic field 41 stability, mathematical 61, 160, 193, 201, 206-208, 217 estimate of 218 Holder stability 218 inverse problems 205, 206, 209 logarithmic 218 statistical edge finding 189 stochastic model 203, 208, 223 surface morphology 190 surface rendering 194 surgery cryosurgery 177, 178, 194 minimally invasive 168 planning 173, 194 robot-assisted 168 thermal surgery 177 tracking during 175 synthesis of parametric images 192 system-related artifacts 29 T temporal regularization 138 temporal resolution 49 tensor tomography 212 therapeutic intervention 167 three-dimensional attenuation correction 118 three-dimensional data acquisition 114, 116

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Page 238 three-dimensional displays 31, 33, 74, 129 three-dimensional reconstruction algorithms 119 three-dimensional sampling 221 three-dimensional visualization 46, 172, 193, 194 thresholding 190 Tikhonov-Phillips regularization method 138, 218, 224 time domain methods 206 time-of-flight information 119 tissue fiber orientation 82 transducer development 122 transmission tomography 199, 202, 203, 216, 221 transport equation 207, 208, 215 transport operator 216 treatment planning 195 U ultrasonics 4 ultrasound 14, 122, 167, 205, 215, 216 instrumentation 122 inverse scattering problem 127 system electronics 124 transducers 123, 180 ultrasound imaging 121, 122, 124, 127, 153, 169, 176, 178 reconstruction with backpropagation method 127 V vectorcardiography (VCG) 134 vector tomography 212 visualization 8, 193 external 8 three-dimensional 46, 172, 193, 194 volume imaging 73 volume rendering 194 W wavelets 56, 61 wave numbers, handling large 207 weighted least squares 100 Wiener filter 100, 101 Wolff-Parkinson-White syndrome 134 X xeromammography 17 x-ray fluoroscopy 167, 168 x-ray projection imaging 13, 14 x-ray sources, monochromatic 34 multiple monochromatic 21 tubes 26, 28, 29, 32, 34 x-ray tomography 208, 216