Computed tomography: algorithms, insight, and just enough theory
"This book is primarily aimed at students, researchers, and practitioners who are interested in the computational aspects of X-ray computed tomography (CT)"--
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
siam, Society for Industrial and Applied Mathematics
[2021]
|
| Schriftenreihe: | Fundamentals of algorithms
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book is primarily aimed at students, researchers, and practitioners who are interested in the computational aspects of X-ray computed tomography (CT)"-- |
| Beschreibung: | xvii, 337 Seiten Illustrationen, Diagramme |
| ISBN: | 9781611976663 1611976669 |
Internformat
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| 245 | 1 | 0 | |a Computed tomography |b algorithms, insight, and just enough theory |c edited by Per Christian Hansen, Technical University of Denmark, Kongens Lyngby, Denmark, Jakob Sauer Jørgensen, Technical University of Denmark, Kongens Lyngby,, William R.B. Lionheart, University of Manchester, Manchester, United Kingdom ; with contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto and Jan Sijbers |
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| 653 | 0 | |a Geometric tomography | |
| 653 | 0 | |a Tomography / Data processing | |
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Datensatz im Suchindex
| _version_ | 1805071246577106944 |
|---|---|
| adam_text |
Contents Preface xi Notation xiii Getting Started with the MATLAB Exercises xvii 1 Introduction 1 P C. Hansen, J. S. Jørgensen, IL R. В. Lionheart 1.1 1.2 1.3 2 Just Enough Analysis: Functions, Operators, and Inverse Problems W R. B. Lionheart 2.1 2.2 2.3 3 A Little History. Tomography Today. Aim and Contents of This Book. Setting the Stage. Inverse Problems and Regularization. The Fourier Transform. Just Enough Linear Algebra 2 3 5 9 10 15 22 27 P C. Hansen 3.1 3.2 4 Systems of Linear Equations . Linear Least-Squares Problems. Just Enough Physics 27 30 35 J. Sijbers, J. S. Jørgensen 4.1 4.2 4.3 4.4 Fundamentals of X-Rays . Interaction with Matter . Detection of X-Rays. Photon Noise. vii 35 39 46 48
Contents viii 5 4.5 Scan Geometries. Exercises. 52 53 The Radon Transform 55 J. S. Jørgensen, IK R. B. Lionheart 6 5.1 Introducing the Radon Transform. 5.2 Basic Properties of the Radon Transform. 5.3 Radon Transform of Simple GeometricShapes. 5.4 Meet the Sinogram. 5.5 Into 3D: The X-Ray Transform. Exercises. 55 59 61 65 68 70 Filtered Back-Projection 73 J. S. Jørgensen, IK R. B. Lionheart 6.1 Back-Projection. 6.2 Fourier Slice Theorem: Key to Reconstruction. 6.3 The Filtered Back-Projection Method. 6.4 The Inverse of the Radon Transform . 6.5 Back-Projection as the Adjoint. 6.6 Stability and Consistency. 6.7 Reconstruction for Fan-Beam Data. 6.8
Reconstruction in 3D with Complete and Cone-Beam Data*. Exercises. 7 Singular Values and Functions of the Radon Transform 73 76 79 87 88 89 93 94 99 105 P. C. Hansen, IK R. B. Lionheart 7.1 Singular Values and Functions. 105 7.2 Derivation of the Singular System for the Radon Transform* . 114 Exercises. 120 8 Limited-Data Tomography 123 E. T. Quinto 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Filtered Back-Projection on Completed Data. 125 Categorizing Singularities and Features of Objects. 126 Visible and Invisible Singularities of the Object . 128 Object-Dependent Artifacts: Artifact Lines Tangent to Boundaries in the Object. 129 Object-Independent Artifacts. 131 Putting It All Together. 135 Another View on Ill-Posedness*. 138 Artifact-Reduced FBP on Completed Data. 138
ix Contents 8,9 Other Algorithms.140 8.10 A Brief Introduction to Microlocal Analysis*. 142 Exercises. 147 9 Discretization Models and the System Matrix 155 K. J. Batenburg, P. C. Hansen, J. S. Jørgensen 9.1 Discretization of Images. 155 9.2 Pixels and Discrete Images.157 9.3 Projection Models.159 9.4 The System Matrix and Its Properties.167 9.5 Using the System Matrix . 174 Exercises. 179 10 SVD Analysis of Tomography Problems 183 P. C. Hansen 10.1 The Singular Value Decomposition. 183 10.2 Ill-Conditioned Problems and Noisy Data. 189 10.3 Spectral Filtering . 191 10.4 SVD Analysis of Discretized CT Problems. 194 10.5 The Role of the Null Space in
Tomography. 202 Exercises. 205 11 Algebraic Iterative Reconstruction Methods 211 P C. Hansen 11.1 Iterative Solvers. 213 11.2 Noisy Data and Semiconvergence.223 Exercises. 239 12 Regularization Techniques for Tomography Problems 251 Y. Dong 12.1 Why Do We Need Regularization?. 251 12.2 Tikhonov Regularization . 252 12.3 Tikhonov Regularization in General Form.261 12.4 Sparsity Regularization. 263 12.5 Total Variation Regularization. 265 Exercises. 269 13 Optimization Methods for Tomography 275 Μ. S. Andersen 13.1 13.2 The Gradient Method. 275 Step Sizes and Stopping Criteria . 292
Contents x 13.3 Gradient Methods for Constrained Optimization. 300 13.4 Regularized Least Squares. 305 Exercises. 312 14 Looking Ahead 317 P. C. Hansen, J. S. Jørgensen, ѴИ R. В. Lionheart Bibliography 319 Index 333 |
| adam_txt |
Contents Preface xi Notation xiii Getting Started with the MATLAB Exercises xvii 1 Introduction 1 P C. Hansen, J. S. Jørgensen, IL R. В. Lionheart 1.1 1.2 1.3 2 Just Enough Analysis: Functions, Operators, and Inverse Problems W R. B. Lionheart 2.1 2.2 2.3 3 A Little History. Tomography Today. Aim and Contents of This Book. Setting the Stage. Inverse Problems and Regularization. The Fourier Transform. Just Enough Linear Algebra 2 3 5 9 10 15 22 27 P C. Hansen 3.1 3.2 4 Systems of Linear Equations . Linear Least-Squares Problems. Just Enough Physics 27 30 35 J. Sijbers, J. S. Jørgensen 4.1 4.2 4.3 4.4 Fundamentals of X-Rays . Interaction with Matter . Detection of X-Rays. Photon Noise. vii 35 39 46 48
Contents viii 5 4.5 Scan Geometries. Exercises. 52 53 The Radon Transform 55 J. S. Jørgensen, IK R. B. Lionheart 6 5.1 Introducing the Radon Transform. 5.2 Basic Properties of the Radon Transform. 5.3 Radon Transform of Simple GeometricShapes. 5.4 Meet the Sinogram. 5.5 Into 3D: The X-Ray Transform. Exercises. 55 59 61 65 68 70 Filtered Back-Projection 73 J. S. Jørgensen, IK R. B. Lionheart 6.1 Back-Projection. 6.2 Fourier Slice Theorem: Key to Reconstruction. 6.3 The Filtered Back-Projection Method. 6.4 The Inverse of the Radon Transform . 6.5 Back-Projection as the Adjoint. 6.6 Stability and Consistency. 6.7 Reconstruction for Fan-Beam Data. 6.8
Reconstruction in 3D with Complete and Cone-Beam Data*. Exercises. 7 Singular Values and Functions of the Radon Transform 73 76 79 87 88 89 93 94 99 105 P. C. Hansen, IK R. B. Lionheart 7.1 Singular Values and Functions. 105 7.2 Derivation of the Singular System for the Radon Transform* . 114 Exercises. 120 8 Limited-Data Tomography 123 E. T. Quinto 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Filtered Back-Projection on Completed Data. 125 Categorizing Singularities and Features of Objects. 126 Visible and Invisible Singularities of the Object . 128 Object-Dependent Artifacts: Artifact Lines Tangent to Boundaries in the Object. 129 Object-Independent Artifacts. 131 Putting It All Together. 135 Another View on Ill-Posedness*. 138 Artifact-Reduced FBP on Completed Data. 138
ix Contents 8,9 Other Algorithms.140 8.10 A Brief Introduction to Microlocal Analysis*. 142 Exercises. 147 9 Discretization Models and the System Matrix 155 K. J. Batenburg, P. C. Hansen, J. S. Jørgensen 9.1 Discretization of Images. 155 9.2 Pixels and Discrete Images.157 9.3 Projection Models.159 9.4 The System Matrix and Its Properties.167 9.5 Using the System Matrix . 174 Exercises. 179 10 SVD Analysis of Tomography Problems 183 P. C. Hansen 10.1 The Singular Value Decomposition. 183 10.2 Ill-Conditioned Problems and Noisy Data. 189 10.3 Spectral Filtering . 191 10.4 SVD Analysis of Discretized CT Problems. 194 10.5 The Role of the Null Space in
Tomography. 202 Exercises. 205 11 Algebraic Iterative Reconstruction Methods 211 P C. Hansen 11.1 Iterative Solvers. 213 11.2 Noisy Data and Semiconvergence.223 Exercises. 239 12 Regularization Techniques for Tomography Problems 251 Y. Dong 12.1 Why Do We Need Regularization?. 251 12.2 Tikhonov Regularization . 252 12.3 Tikhonov Regularization in General Form.261 12.4 Sparsity Regularization. 263 12.5 Total Variation Regularization. 265 Exercises. 269 13 Optimization Methods for Tomography 275 Μ. S. Andersen 13.1 13.2 The Gradient Method. 275 Step Sizes and Stopping Criteria . 292
Contents x 13.3 Gradient Methods for Constrained Optimization. 300 13.4 Regularized Least Squares. 305 Exercises. 312 14 Looking Ahead 317 P. C. Hansen, J. S. Jørgensen, ѴИ R. В. Lionheart Bibliography 319 Index 333 |
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| isbn | 9781611976663 1611976669 |
| language | English |
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| spelling | Computed tomography algorithms, insight, and just enough theory edited by Per Christian Hansen, Technical University of Denmark, Kongens Lyngby, Denmark, Jakob Sauer Jørgensen, Technical University of Denmark, Kongens Lyngby,, William R.B. Lionheart, University of Manchester, Manchester, United Kingdom ; with contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto and Jan Sijbers Philadelphia siam, Society for Industrial and Applied Mathematics [2021] xvii, 337 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Fundamentals of algorithms 21 "This book is primarily aimed at students, researchers, and practitioners who are interested in the computational aspects of X-ray computed tomography (CT)"-- Dreidimensionale Rekonstruktion (DE-588)4150634-0 gnd rswk-swf Regularisierung (DE-588)4124043-1 gnd rswk-swf Singulärwertzerlegung (DE-588)4348101-2 gnd rswk-swf Computertomografie (DE-588)4113240-3 gnd rswk-swf Geometric tomography Tomography / Data processing Computertomografie (DE-588)4113240-3 s Regularisierung (DE-588)4124043-1 s Singulärwertzerlegung (DE-588)4348101-2 s Dreidimensionale Rekonstruktion (DE-588)4150634-0 s DE-604 Hansen, Per Christian 1957- Sonstige (DE-588)12198379X oth Erscheint auch als Online-Ausgabe, EPUB 9781611976670 Fundamentals of algorithms 21 (DE-604)BV017480576 18 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033188011&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Computed tomography algorithms, insight, and just enough theory Fundamentals of algorithms Dreidimensionale Rekonstruktion (DE-588)4150634-0 gnd Regularisierung (DE-588)4124043-1 gnd Singulärwertzerlegung (DE-588)4348101-2 gnd Computertomografie (DE-588)4113240-3 gnd |
| subject_GND | (DE-588)4150634-0 (DE-588)4124043-1 (DE-588)4348101-2 (DE-588)4113240-3 |
| title | Computed tomography algorithms, insight, and just enough theory |
| title_auth | Computed tomography algorithms, insight, and just enough theory |
| title_exact_search | Computed tomography algorithms, insight, and just enough theory |
| title_exact_search_txtP | Computed tomography algorithms, insight, and just enough theory |
| title_full | Computed tomography algorithms, insight, and just enough theory edited by Per Christian Hansen, Technical University of Denmark, Kongens Lyngby, Denmark, Jakob Sauer Jørgensen, Technical University of Denmark, Kongens Lyngby,, William R.B. Lionheart, University of Manchester, Manchester, United Kingdom ; with contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto and Jan Sijbers |
| title_fullStr | Computed tomography algorithms, insight, and just enough theory edited by Per Christian Hansen, Technical University of Denmark, Kongens Lyngby, Denmark, Jakob Sauer Jørgensen, Technical University of Denmark, Kongens Lyngby,, William R.B. Lionheart, University of Manchester, Manchester, United Kingdom ; with contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto and Jan Sijbers |
| title_full_unstemmed | Computed tomography algorithms, insight, and just enough theory edited by Per Christian Hansen, Technical University of Denmark, Kongens Lyngby, Denmark, Jakob Sauer Jørgensen, Technical University of Denmark, Kongens Lyngby,, William R.B. Lionheart, University of Manchester, Manchester, United Kingdom ; with contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto and Jan Sijbers |
| title_short | Computed tomography |
| title_sort | computed tomography algorithms insight and just enough theory |
| title_sub | algorithms, insight, and just enough theory |
| topic | Dreidimensionale Rekonstruktion (DE-588)4150634-0 gnd Regularisierung (DE-588)4124043-1 gnd Singulärwertzerlegung (DE-588)4348101-2 gnd Computertomografie (DE-588)4113240-3 gnd |
| topic_facet | Dreidimensionale Rekonstruktion Regularisierung Singulärwertzerlegung Computertomografie |
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