Index for Principles of Computerized Tomographic Imaging

This is an index for the book "Principles of Computerized Tomographic Imaging" by A. C. Kak and Malcolm Slaney. Each page number in this index is linked to the appropriate chapter. Each chapter is stored as a PDF file, ranging in size from 2 to 10 M bytes each.

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A. C. Kak and Malcolm Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, 1988.

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The Table of Contents for this book is available at http://www.slaney.org/pct/index.html

A

Algebraic equations
      solution by Kaczmarz method 278
Algebraic reconstruction techniques 283-284
      sequential 289, 293
      simultaneous 285-292
Algebraic techniques
      reconstruction algorithms 275-296
Algorithms
      cone beams 104
      filtered backprojection 60-63, 72, 104
      filtered backpropagation 234-247
      Gerchberg-Papoulis 313-314
      reconstruction 49-112, 252-261, 275-296, 313-320
      re-sorting 92-93
      SIRT 295
      see also Reconstruction algorithms
Aliasing
      artifacts 177-201
      bibliography 200
      in 2-D images 46
      properties 177-186
Approximations
      Born 212-214, 248-253
      comparison 248-252
      Rytov 214-218, 249-253
      to wave equation 214-218
ART see Algebraic reconstruction techniques
Artifacts
      aliasing 177-201
      beam hardening 124
      bibliography 200
      polychromaticity 120-125
Attenuation compensation
      for positron tomography 145-147
      for single photon emission CT 137-142
Authors
      affiliations 329
      Kak AvinashC., 329
      Slaney Malcolm, 329

B

Backprojection 179
      filtered 60-63, 65-72, 82, 84-85, 88, 104-107
      star-shaped pattern 184
      weighted 92, 106
      3-D 104-107
Backpropagation algorithm 242-247, 262
      filtered 234-247
Bandlimited filter
      DFT 74
Beam hardening 118
      artifacts 120, 124
Bibliographic notes
      algebraic reconstruction algorithms 292-295
      algorithms for reconstructions with non-diffracting sources 107-110
      aliasing artifacts and noise in CT images 200
      measurement of projection data nondiffractingcase, 168-169
      reflection tomography 321
      tomographic imaging with diffracting sources 268-270
Bones 122
      Born approximation 215-218, 249-253, 258
      evaluation 24849
      first 212-214
Breasts
      mammograms 159
      sonograms 302
      B-scan imaging 297-303, 315
      commercial 302

C

Cancer
      in breast 159-160
Carcinoma
      sonogram 302
Coincidence testing
      circuits 143
      of positron emission 143
Collinear detectors
      equally spaced 86-92
Compton effect 114-115, 119
Computed tomography see Computerized tomography
Computerized tomography
      applications 132-133
      emission 134-147, 275
      graduate courses ix
      images 177-201
      noise 177-201
      scanners 130
      ultrasonic 147-158
      x-rays 120-124
Cone beams
      algorithms 104, 108-109
      projection 101
      reconstruction 102, 108-109
Continuous signals
      Fourier analysis 11
Convolution 8-9, 31-32, 83
      aperiodic 18
      calculation 15
      circular 18, 66
      Fourier transforms 39
CT see Computerized tomography

D

Data collection process 228-234
Data definition
      negative time 25-26
      positive time 26
Data sequences 26
      padding 23-25
      resolution 23
Data truncation
      effects 27-28
Delta functions 28-30
      see also Dirac delta
Detectors 75, 101, 127, 192
      arrays 188
      collinear 86-92
      equal spacing 86-92
      ray paths 190
      spacing 78, 188
      xenon gas 128
DFT see Fourier transforms-discrete
Diffracting sources
      filtered backpropagation algorithm 234-247
      interpolation 234-247
      tomographic imaging 203-273
Diffraction tomography reconstructions
      limitations 247-251
Dirac delta 5-7, 12, 30, 32, 222
      see also Delta functions
Display resolution
      in freauencv domain 22-27
Distortions
      aliasing 177-201
Dogs
      heart 154, 156-157

E

Education
      graduate ix
Emission computer tomography 134-147
Equiangular rays 77-86
Equispaced detectors
      collinear 86-92
      reconstruction algorithms 87
Evanescent waves 261
      ignoring 266

F

Fan beam reconstruction
      from limited number of views 93-99
Fan beams 78, 85
      projections 97
      reconstruction 93-99
      re-sorting 92
      rotation 126
      scanners 188
      tilted 105
Fan projections
      reconstruction 75-93
FFT (Fast Fourier Transforms)
      inverse 42, 240
      l-D 45
      2-D 45-47
FFT output
      interpretation 20-22
Filters and filtering 7
      backprojection 60-63, 65, 68, 72, 82, 84-85, 88, 104-107
      backpropagation 234-247
      bandlimited 74
      ideal 72
      low pass 40-41, 266
      shift invariant 8
      Wiener 306
Finite receiver length
      effects 263-266
      experiments 266
      reconstruction 266
Forward projection process
      modeling 286-288
Fourier analysis
      of function 9-13, 33-35
      Fourier diffraction theorem 218-234, 253-254, 259
      short wavelength limit 227-228
      Fourier series -13
      triangle wave 12
      Fourier slice theorem 228, 260, 307
      tomographic imaging 49, 56-61
Fourier transforms
      diffraction 219, 223-227
      discrete 10, 13-15
      fast 16, 18, 20-26
      finite 10, 16-18, 42-45
      generalized 13
      inverse 13, 17, 34-35, 42, 226
      line integrals 318
      Parseval's theorem 39, 44
      properties 35-41
      seismic profiling 233
      1-D 44-45, 56
      2-D 34-35, 42-45, 222, 226-227, 229, 308
Frequency-shift method 156-158
Functions
      continuous 5-7
      discrete 5-7
      Fourier representation 9-13
      Green's 220-223
      Hankel 220
      linear operations 7-9
      point spread 29, 32
      1-D 5-7

G

Gibbs phenomenon 178
Green's function
      decomposition 220-223
Grids
      representation 277
      square 276
      superimposition 276

H

Haunsfield G.N., -2, 107
Head phantom
      of Shepp and Logan 51-53, 69, 103, 198, 255, 259, 285
Helmholtz equation 224
Hilbert transforms 68
Homogeneous wave equation 204-208
      acoustic pressure field 204
      electromagnetic field 204
Human body
      x-ray propagation 116, 195
Hyperplanes 279

I

Ideal filter 72
      DFT 74
Image processing 28-47
      Fourier analysis 33-35
      graduate courses ix
Images and imaging 276-283
      B-scan 297-303, 315
      CT 177-201
      magnetic resonance 158-168
      noise 177-201
      radar 298-299
      reconstructed 190-194, 281
      sagittal 137
      SPECT 136
Impulse response
      convolution 9
      of ideal filter 73
      of shift invariant filter 8-9
Inhomogeneous wave equation 208-211
      acoustics 209
      electromagnetic case 208
Interpolation
      diffracting sources 234-247
      frequency domain 236-242

K

Kaczmarz method
      for solving algebraic equations 278
      Kak AvinashC.(Author)
      affiliations 329

L

Limitations
      diffraction tomography reconstruction 247-252
      experimental 261-268
      mathematical 247-248
      receivers 268-270
      reflection tomography 309-313
Line integrals 49-56
      Fourier transforms 3, 18

M

Magnetic moments 163
Magnetic resonance imaging 158-168
Mammograms
      of female breasts 159
Medical industry
      use of x-ray tomography 132, 168
Modeling
      forward projection process 286-288
Moire effect 46, 178
MRI see Magnetic resonance imaging

N

Negative time
      of data 25-26
Noise
      in CT images 177-201
      in reconstructed images 190-199
Nondestructive testing
      use of CT 133
Nondiffracting sources
      measurement of projection data 113-174
      reconstruction 49-112
Nyquist rate 19-20, 180

O

Objects
      blurring 192
      broadband illumination 235
      Fourier transforms 166, 235, 239
      illumination 300, 304
      projections 50, 59, 165, 182, 239
      reflectivity 300
Operators and operations
      linear 7-9, 30-32
      shift invariant 8, 30-32

P

Parallel projections
      reconstruction algorithms 60-75
Parseval's theorem
      Fourier transforms 39, 44
Pencil beam
      of energy 299
Phantoms 122
      reconstruction 198, 262
      x-rays 127
Photoelectric effect 114, 119
Photons
      emission 146
      emission tomography 135-137
      gamma-rays 135, 138
Plane waves
      propagation 207
Point sources 28-30
Polychromaticity artifacts
      in x-ray CT 120-125
Polychromatic sources
      for measuring projection data 117-120
Positron emission tomography 142-145
Positron tomography
      attenuation compensation 145-147
Projection data
      measurement 113-174
      sound waves 113
      ultrasound 113
      x-rays 113
Projections 49-56
      backpropagation 245
      cone beam 101
      curved lines 95
      diffracted 204-211
      fan beams 75-93, 97, 192
      forward 286-288
      of cylinders 2
      of ellipse 54, 62
      of objects 50, 59, 165, 182, 239
      parallel 51, 60-75, 77, 100, 185
      representation 276-283
      uniform sampling 238
      x-ray 114-116
      3-D 100-104, 165

R

Radar
      imaging 298-299
Radioactive isotopes
      use in emission CT 134-135
Radon transforms 50, 52, 93-97
Received waves
      sampling 261-262
Receivers
      effect of finite length 263-266
      limited views 268-270
Reconstructed images
      continuous case 190-194
      discrete case 194-199
      noise 190-199
Reconstruction
      algebraic 280, 283-292
      algorithms 49-112
      bones 122
      circular 287
      cone beams 102
      cylinders 256, 310
      diffraction tomography 247
      dog's heart 154, 156-157
      errors 177-201
      fan beams 93-99
      from fan projections 75-93
      iterative 284, 289-290
      large-sized 282
      limitations 261-268
      of ellipse 178, 181
      of images 83, 122, 198, 281
      of Shepp and Logan phantom 70
      phantom 198
      plane wave reflection 310
      refractive index 154
      simultaneous 284-292
      tumors 290, 294
      with nondiffracting sources 49-112
      2-D 100
      3-D 99-107
Reconstruction algorithms 13-20
      algebraic 275-296
      cone beams 103, 108-109
      evaluation 252-261
      for equispaced detectors 87
      for parallel projections 60-75
      implementation 288-292
Rectangle function
      limit 29
      2-D Fourier transform 34
Reflection tomography 297-322
      experimental results 320-321
      limits 309-313
      of needles 320
      transducers 307
      vs. diffraction tomography 307-309
      with basic aim 297
      with point transmitter/receivers 313-321
Refractive index tomography
      ultrasonic 151-153
Re-sorting
      algorithm 92-93
      of fan beams 92
Rocket motors
      nondestructive testing 133-134
      Rytov approximation 249-253, 258
      evaluation 249
      first 214-218

S

Sampling
      in real system 186-189
      of data 19-20
      of projection 238
      received waves 261-262
SART see Simultaneous algebraic reconstruction technique
Scanning and scanners
      B-scan imaging 297-303
      CT 130
      different methods 126-132
      fan beams 188
      fourth generation 129
Scattering
      x-rays 125-126
Seismic profiling
      experiment 232
      Fourier transforms 233
Shift invariant operations linear 30-32
Short wavelength limit of Fourier diffraction theorem 227-228
Signal processing
      fundamentals 5
      graduate courses ix
      one-dimensional 5
Simultaneous algebraic reconstruction technique 285-292
      implementation 288
Simultaneous iterative reconstructive technique 284
      algorithm 295
Single photon emission tomography 135-137
      attenuation compensation 137-142
Sinograms 94
SIRT see Simultaneous iterative reconstructive technique
Skull
      simulated 121
      Slaney Malcolm(Author)
      affiliations 329
Sonograms
      of breast 302
      of carcinoma 302
Sound waves
      projection data 113
      SPECT images 136
Synthetic aperture
      tomography 230-231

T

Tomography
      applications 1
      definition 1
      diffraction 203, 221, 247, 307-309
      emission computed 134-147, 275
      Fourier slice theorem 49, 56-61
      imaging with diffracting sources 203-273
      positron 145-147
      positron emission 142-145
      reflection 297-322
      simulations 55
      synthetic aperture 230-231
      ultrasonic 147-158, 205
      x-ray -3, 114-133
      x-ray scanner 1, 107
      3-D simulations 102
      see also Computerized tomography, Reflection tomography, Single photon emission tomography, Ultrasonic computed tomography
Transducers
      plane wave 303-307
      pulse illumination 312
      reflection 303-307
      rotation 316
      ultrasonic 149
Transforms see Fourier transforms, Hilbert transforms, Radon transforms
Transmitter/receivers
      point 313-321
      reflection tomography 313-321
Tumors
      reconstruction 290-294

U

Ultrasonic beams
      propagation 149, 153
Ultrasonic computed tomography 147-158
      applications 157-158
      attenuation 153-157
      fundamentals 148-151
      refractive index 151-153
Ultrasonic signals 152-153

W

Wave equation
      approximations 211-218
      homogeneous 204-208
      inhomogeneous 208-211
Weighting functions 99
      backprojection 92
Windows
      Hamming 291, 293-294
      smooth 98

X

X-rays
      CT 120-125
      in human body 195
      monochromatic 114-116
      parallel beams 116
      phantoms 127
      photons 128
      projection data 113
      scatter 125-126
      sources 129
      tomography 114-133
      tubes 115