**Suggested Citation:**"INDEX." National Research Council. 1996.

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### 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

patient-related 29

physics-related 28

ring-shaped 29

system-related 29

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

compensation 99

distribution, non-uniform 91, 99

distribution, uniform 99

linear 24

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 hardening 25, 28, 30, 200

artifacts 25

beam propagation 123

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

imaging of 37

blood oxygen level dependent (BOLD) effect 69

Born approximation 205

#### C

cardiac strain 67

chemical shift imaging 75

cluster analysis 189

partial-volume 50

superconducting 79

**Suggested Citation:**"INDEX." National Research Council. 1996.

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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

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

high-speed 30

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

#### 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

multi-dimensional 187

three-dimensional 31, 33, 74, 129

data fusion 188

data interpolation 31

data sampling 117

data visualization 188

detector systems

efficiency 108

noise in 153

ring-based 28

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

application to strokes 81

diffusion tensor imaging (DTI) 81

digital subtraction angiography (DSA) 13

discrete Fourier transform 40

**Suggested Citation:**"INDEX." National Research Council. 1996.

*Mathematics and Physics of Emerging Biomedical Imaging*. Washington, DC: The National Academies Press. doi: 10.17226/5066.

Page 233

Doppler shift 211

#### 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

endocardial potentials 135

expectation maximization algorithm 99, 113

#### F

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

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

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

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

global thresholding 189

for MRI 49

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

**Suggested Citation:**"INDEX." National Research Council. 1996.

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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

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 radiology 168

inverse problem 113, 114, 135-137, 148, 202, 205, 206, 208, 209, 214-216, 224

inversion algorithms for EIT 144

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 RF coils 50

logarithmic stability 218

magnetic field gradients 70

**Suggested Citation:**"INDEX." National Research Council. 1996.

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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

magnetic field for 41

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

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 receivers 48

#### N

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

photon attenuation and scatter 97

physics-related artifacts 28

positron emission tomography (PET) 3, 105-114, 117, 119, 148, 159, 160, 203

**Suggested Citation:**"INDEX." National Research Council. 1996.

*Mathematics and Physics of Emerging Biomedical Imaging*. Washington, DC: The National Academies Press. doi: 10.17226/5066.

Page 236

PET (continued)

data corrections 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

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

Radon inversion formula 200

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

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

ESI 135

MSI 152

PET 110

spatial 23, 31, 33, 49, 51, 56, 58, 59, 90, 92, 94-96, 110, 135, 144, 152

restoration filter 100

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

**Suggested Citation:**"INDEX." National Research Council. 1996.

*Mathematics and Physics of Emerging Biomedical Imaging*. Washington, DC: The National Academies Press. doi: 10.17226/5066.

Page 237

scattering (continued)

correction/compensation 20, 100, 117, 118

response function 100

scintillation crystals 108

*see also detector elements*

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

single photon emission computed tomography (SPECT) 7, 90-94, 96-102, 148, 159, 160, 203

brain 93

converging-beam 102

dynamic 93

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

semiconductor 95

silicon 95

SPECT image reconstruction 91, 96-99

iterative methods 99

limited-angle 101

SPECT system design—see SPECT instrumentation 93

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

minimally invasive 168

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

**Suggested Citation:**"INDEX." National Research Council. 1996.

*Mathematics and Physics of Emerging Biomedical Imaging*. Washington, DC: The National Academies Press. doi: 10.17226/5066.

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

ultrasound imaging 121, 122, 124, 127, 153, 169, 176, 178

reconstruction with backpropagation method 127

#### V

vectorcardiography (VCG) 134

vector tomography 212

external 8

three-dimensional 46, 172, 193, 194

volume imaging 73

volume rendering 194

#### W

wave numbers, handling large 207

weighted least squares 100

Wolff-Parkinson-White syndrome 134

#### X

xeromammography 17

x-ray projection imaging 13, 14

x-ray sources,

monochromatic 34

multiple monochromatic 21