Principles of computerized tomographic imaging:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, Pa.
Soc. for Industrial and Applied Mathematics
2001
|
| Edition: | Unabridged republ. |
| Series: | Classics in applied mathematics
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 327 S. Ill., graph. Darst. |
| ISBN: | 089871494X 9780898714944 |
Staff View
MARC
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| 245 | 1 | 0 | |a Principles of computerized tomographic imaging |c Avinash C. Kak ; Malcolm Slaney |
| 250 | |a Unabridged republ. | ||
| 264 | 1 | |a Philadelphia, Pa. |b Soc. for Industrial and Applied Mathematics |c 2001 | |
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Record in the Search Index
| _version_ | 1804128757925019648 |
|---|---|
| adam_text | Contents
Preface to the Classics Edition xi
Preface xiii
1 Introduction 1
References 3
2 Signal Processing Fundamentals 5
2.1 One Dimensional Signal Processing S
Continuous and Discrete One Dimensional Functions • Linear
Operations • Fourier Representation • Discrete Fourier Transform
(DFT) • Finite Fourier Transform • Just How Much Data Is Needed? •
Interpretation of the FFT Output • How to Increase the Display
Resolution in the Frequency Domain • How to Deal with Data Defined
for Negative Time • How to Increase Frequency Domain Display
Resolution of Signals Defined for Negative Time • Data Truncation
Effects
2.2 Image Processing 28
Point Sources and Delta Functions • Linear Shift Invariant Operations •
Fourier Analysis • Properties of Fourier Transforms • The
Two Dimensional Finite Fourier Transform • Numerical Implementation
of the Two Dimensional FFT
2.3 References 47
3 Algorithms for Reconstruction with Nondiffracting Sources 49
3.1 Line Integrals and Projections 49
3.2 The Fourier Slice Theorem 56
3.3 Reconstruction Algorithms for Parallel Projections 60
The Idea • Theory • Computer Implementation of the Algorithm
3.4 Reconstruction from Fan Projections 75
Equiangular Rays • Equally Spaced Collinear Detectors • A Re sorting
Algorithm
3.5 Fan Beam Reconstruction from a Limited Number of Views 93
3.6 Three Dimensional Reconstructions 99
Three Dimensional Projections • Three Dimensional Filtered
Backprojection
vii
3.7 Bibliographic Notes 107
3.8 References 110
4 Measurement of Projection Data—The Nondiffracting Case 113
4.1 X Ray Tomography 114
Monochromatic X Ray Projections • Measurement of Projection Data
with Polychromatic Sources • Polychromaticity Artifacts in X Ray CT •
Scatter • Different Methods for Scanning • Applications
4.2 Emission Computed Tomography 134
Single Photon Emission Tomography • Attenuation Compensation for
Single Photon Emission CT • Positron Emission Tomography •
Attenuation Compensation for Positron Tomography
4.3 Ultrasonic Computed Tomography 147
Fundamental Considerations • Ultrasonic Refractive Index Tomography
• Ultrasonic Attenuation Tomography • Applications
4.4 Magnetic Resonance Imaging 158
4.5 Bibliographic Notes 168
4.6 References 169
5 Aliasing Artifacts and Noise in CT Images 177
5.1 Aliasing Artifacts 177
What Does Aliasing Look Like? • Sampling in a Real System
5.2 Noise in Reconstructed Images 190
The Continuous Case • The Discrete Case
5.3 Bibliographic Notes 200
5.4 References 200
6 Tomographic Imaging with Diffracting Sources 203
6.1 Diffracted Projections 204
Homogeneous Wave Equation • Inhomogeneous Wave Equation
6.2 Approximations to the Wave Equation 211
The First Born Approximation • The First Rytov Approximation
6.3 The Fourier Diffraction Theorem 218
Decomposing the Green s Function • Fourier Transform Approach •
Short Wavelength Limit of the Fourier Diffraction Theorem • The Data
Collection Process
6.4 Interpolation and a Filtered Backpropagation Algorithm for Diffracting
Sources 234
Frequency Domain Interpolation • Backpropagation Algorithms
viii
6.5 Limitations 247
Mathematical Limitations • Evaluation of the Bom Approximation •
Evaluation of the Rytov Approximation • Comparison of the Born and
Rytov Approximations
6.6 Evaluation of Reconstruction Algorithms 252
6.7 Experimental Limitations 261
Evanescent Waves • Sampling the Received Wave • The Effects of a
Finite Receiver Length • Evaluation of the Experimental Effects •
Optimization • Limited Views
6.8 Bibliographic Notes 268
6.9 References 270
7 Algebraic Reconstruction Algorithms 275
7.1 Image and Projection Representation 276
7.2 ART (Algebraic Reconstruction Techniques) 283
7.3 SIRT (Simultaneous Iterative Reconstructive Technique) 284
7.4 SART (Simultaneous Algebraic Reconstruction Technique) 285
Modeling the Forward Projection Process • Implementation of the
Reconstruction Algorithm
7.5 Bibliographic Notes 292
7.6 References 295
8 Reflection Tomography 297
8.1 Introduction 297
8.2 B Scan Imaging 298
8.3 Reflection Tomography 303
Plane Wave Reflection Transducers • Reflection Tomography vs.
Diffraction Tomography • Reflection Tomography Limits
8.4 Reflection Tomography with Point Transmitter/Receivers 313
Reconstruction Algorithms • Experimental Results
8.5 Bibliographic Notes 321
8.6 References 321
Index 323
ix
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| bvnumber | BV013914978 |
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| discipline | Informatik Medizintechnik Medizin |
| edition | Unabridged republ. |
| format | Book |
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| id | DE-604.BV013914978 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:19Z |
| institution | BVB |
| isbn | 089871494X 9780898714944 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009520893 |
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| physical | XIV, 327 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Soc. for Industrial and Applied Mathematics |
| record_format | marc |
| series | Classics in applied mathematics |
| series2 | Classics in applied mathematics |
| spelling | Kak, Avinash C. 1944- Verfasser (DE-588)1215360487 aut Principles of computerized tomographic imaging Avinash C. Kak ; Malcolm Slaney Unabridged republ. Philadelphia, Pa. Soc. for Industrial and Applied Mathematics 2001 XIV, 327 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in applied mathematics 33 1988 Computertomografie (DE-588)4113240-3 gnd rswk-swf Tomografie (DE-588)4078351-0 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Computertomografie (DE-588)4113240-3 s Bildverarbeitung (DE-588)4006684-8 s DE-604 Tomografie (DE-588)4078351-0 s Slaney, Malcolm Verfasser (DE-588)1215361327 aut Reproduktion von New York : IEEE Press, 1988 0-87942-198-3 (DE-604)BV006566661 Classics in applied mathematics 33 (DE-604)BV008258410 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009520893&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kak, Avinash C. 1944- Slaney, Malcolm Principles of computerized tomographic imaging Classics in applied mathematics Computertomografie (DE-588)4113240-3 gnd Tomografie (DE-588)4078351-0 gnd Bildverarbeitung (DE-588)4006684-8 gnd |
| subject_GND | (DE-588)4113240-3 (DE-588)4078351-0 (DE-588)4006684-8 |
| title | Principles of computerized tomographic imaging |
| title_auth | Principles of computerized tomographic imaging |
| title_exact_search | Principles of computerized tomographic imaging |
| title_full | Principles of computerized tomographic imaging Avinash C. Kak ; Malcolm Slaney |
| title_fullStr | Principles of computerized tomographic imaging Avinash C. Kak ; Malcolm Slaney |
| title_full_unstemmed | Principles of computerized tomographic imaging Avinash C. Kak ; Malcolm Slaney |
| title_short | Principles of computerized tomographic imaging |
| title_sort | principles of computerized tomographic imaging |
| topic | Computertomografie (DE-588)4113240-3 gnd Tomografie (DE-588)4078351-0 gnd Bildverarbeitung (DE-588)4006684-8 gnd |
| topic_facet | Computertomografie Tomografie Bildverarbeitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009520893&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008258410 |
| work_keys_str_mv | AT kakavinashc principlesofcomputerizedtomographicimaging AT slaneymalcolm principlesofcomputerizedtomographicimaging |