The Radon transform and some of its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1983
|
| Series: | A Wiley-Interscience publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 247 - 281 |
| Physical Description: | XI, 289 S. graph. Darst. |
| ISBN: | 047189804X |
Staff View
MARC
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| 100 | 1 | |a Deans, Stanley Roderick |d 1937- |e Verfasser |0 (DE-588)172038944 |4 aut | |
| 245 | 1 | 0 | |a The Radon transform and some of its applications |c Stanley R. Deans |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1983 | |
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Record in the Search Index
| _version_ | 1804116446849007616 |
|---|---|
| adam_text | Contents
Chapter 1. Major Fields of Application, 1
[1.1] Introduction 1
[1.2] Medicine; X ray Computed Tomography 11
[1.3] Medicine; Emission Computed Tomography 16
[1.4] Medicine; Ultrasound CT 21
[1.5] Astronomy 24
[1.6] Electron Microscopy 31
[1.7] Nuclear Magnetic Resonance 35
[1.8] Optics 42
[1.9] Stress Analysis, Geophysics, and Other Areas 48
[1.10] References 50
Chapter 2. Definition of the Radon Transform, 55
[2.1] Introduction 55
[2.2] Two Dimensions 56
[2.3] Three Dimensions 59
[2.4] Extension to Higher Dimensions 60
[2.5] Some Important Examples 61
Chapter 3. Basic Properties, 66
[3.1] Introduction 66
[3.2] Homogeneity 66
[3.3] Linearity 67
[3.4] Transform of a Linear Transformation 68
[3.5] Shifting Property 71
[3.6] Transform of Derivatives 77
[3.7] Transforms Involving Hermite Polynomials 80
[3.8] Transforms Involving Laguerre Polynomials 86
[3.9] Derivatives of the Transform 91
[3.10] Transform of Convolution 94
ix
x CONTENTS
Chapter 4. Relation to Other Transforms, 96
[4.1] Introduction 96
[4.2] Relation to the Fourier Transform 96
[4.3] Relation to the Gegenbauer Transform 100
[4.4] Relation to the Hough Transform 106
Chapter 5. Inversion, 108
[5.1] Introduction 108
[5.2] Odd Dimension 108
[5.3] Even Dimension 112
[5.4] Unification and the Adjoint 115
[5.5] Fourier Methods 121
Chapter 6. Recent Development of Inversion Methods, 125
[6.1] Introduction 125
[6.2] Projection Slice Theorem 128
[6.3] Backprojection 131
[6.4] Backprojection of Filtered Projections 136
[6.5] Filter of Backprojections 140
[6.6] Iterative Methods 142
[6.7] Three dimensional Methods 147
[6.8] Categorized References 147
Chapter 7. Series Methods, 151
[7.1] Introduction 151
[7.2] Gegenbauer Transform Pair 151
[7.3] Circular Harmonic Expansion (« = 2) 152
[7.4] Spherical Harmonic Expansion (n = 3) 160
[7.5] A Tchebycheff Transform Pair of the Second Kind 163
[7.6] Orthogonal Function Expansions on the Unit Disk 163
[7.7] Orthogonal Function Expansions Over the Entire Plane 180
[7.8] Other Approaches 182
Chapter 8. More Properties, Applications, and Generalizations, 184
[8.1] Introduction 184
[8.2] Characterization of the Transform 184
[8.3] A Discrete Version 187
[8.4] Picture Restoration 191
[8.5] Transformations in Geophysics 192
[8.6] The Integral Equation of Potential Scattering 196
CONTENTS xi
[8.7] Partial Differential Equations 198
[8.8] Generalizations and Other Uses 201
Appendix A. Translation of Radon s 1917 Paper, 204
Appendix B. Generalized Functions, 218
Appendix C. Special Functions, 240
References, 247
Index, 283
|
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| dewey-full | 515.7/23 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 516 - Geometry |
| dewey-raw | 515.7/23 516.3/6 |
| dewey-search | 515.7/23 516.3/6 |
| dewey-sort | 3515.7 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T15:38:39Z |
| institution | BVB |
| isbn | 047189804X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001304187 |
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| physical | XI, 289 S. graph. Darst. |
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| publisher | Wiley |
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| series2 | A Wiley-Interscience publication |
| spelling | Deans, Stanley Roderick 1937- Verfasser (DE-588)172038944 aut The Radon transform and some of its applications Stanley R. Deans New York [u.a.] Wiley 1983 XI, 289 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Literaturverz. S. 247 - 281 Radon, Transformations de Radon transforms Radon-Transformierte (DE-588)4195862-7 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 s DE-604 Radon-Transformierte (DE-588)4195862-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304187&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deans, Stanley Roderick 1937- The Radon transform and some of its applications Radon, Transformations de Radon transforms Radon-Transformierte (DE-588)4195862-7 gnd Radon-Transformation (DE-588)4479199-9 gnd |
| subject_GND | (DE-588)4195862-7 (DE-588)4479199-9 |
| title | The Radon transform and some of its applications |
| title_auth | The Radon transform and some of its applications |
| title_exact_search | The Radon transform and some of its applications |
| title_full | The Radon transform and some of its applications Stanley R. Deans |
| title_fullStr | The Radon transform and some of its applications Stanley R. Deans |
| title_full_unstemmed | The Radon transform and some of its applications Stanley R. Deans |
| title_short | The Radon transform and some of its applications |
| title_sort | the radon transform and some of its applications |
| topic | Radon, Transformations de Radon transforms Radon-Transformierte (DE-588)4195862-7 gnd Radon-Transformation (DE-588)4479199-9 gnd |
| topic_facet | Radon, Transformations de Radon transforms Radon-Transformierte Radon-Transformation |
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