Computed Tomography (eBook)

From Photon Statistics to Modern Cone-Beam CT

Thorsten M. Buzug (Autor)

eBook Download: PDF

2008 | 2008
XIV, 522 Seiten
Springer Berlin (Verlag)
978-3-540-39408-2 (ISBN)

Infos

This volume provides an overview of X-ray technology and the historical development of modern CT systems. The main focus of the book is a detailed derivation of reconstruction algorithms in 2D and modern 3D cone-beam systems. A thorough analysis of CT artifacts and a discussion of practical issues such as dose considerations give further insight into current CT systems. Although written mainly for graduate students, practitioners will also benefit from this book.

Inhalt

Preface 5
Contents 8
1 Introduction 13
1.1 Computed Tomography – State of the Art 13
1.2 Inverse Problems 14
1.3 Historical Perspective 16
1.4 Some Examples 19
1.5 Structure of the Book 23
2 FundamentalsofX-rayPhysics 26
2.1 Introduction 26
2.2 X- ray Generation 26
2.3 Photon–Matter Interaction 42
2.4 Problems with Lambert–Beer’s Law 57
2.5 X- ray Detection 59
2.6 X- ray Photon Statistics 70
3 Milestones of Computed Tomography 85
3.1 Introduction 85
3.2 Tomosynthesis 86
3.3 Rotation– Translation of a Pencil Beam(First Generation) 89
3.4 Rotation– Translation of a Narrow Fan Beam (Second Generation) 93
3.5 Rotation of aWide Aperture Fan Beam ( Third Generation) 94
3.6 Rotation–Fix with Closed Detector Ring (Fourth Generation) 97
3.7 Electron BeamComputerized Tomography 99
3.8 Rotation in Spiral Path 100
3.9 Rotation in Cone-BeamGeometry 101
3.10 Micro- CT 103
3.11 PET- CT Combined Scanners 106
3.12 Optical Reconstruction Techniques 108
4 Fundamentals of Signal Processing 110
4.1 Introduction 111
4.2 Signals 111
4.3 Fundamental Signals 111
4.4 Systems 113
4.5 Signal Transmission 115
4.6 Dirac’s Delta Distribution 118
4.7 Dirac Comb 121
4.8 Impulse Response 124
4.9 Transfer Function 125
4.10 Fourier Transform 127
4.11 Convolution Theorem 133
4.12 Rayleigh’s Theorem 134
4.13 Power Theorem 134
4.14 Filtering in the Frequency Domain 135
4.15 Hankel Transform 137
4.16 Abel Transform 141
4.17 Hilbert Transform 142
4.18 Sampling Theoremand Nyquist Criterion 144
4.19 Wiener–Khintchine Theorem 150
4.20 Fourier Transform of Discrete Signals 153
4.21 Finite Discrete Fourier Transform 154
4.22 z- Transform 156
4.23 Chirp z- Transform 157
5 Two-Dimensional Fourier-Based ReconstructionMethods 160
5.1 Introduction 160
5.2 Radon Transformation 162
5.3 Inverse Radon Transformation and Fourier Slice Theorem 172
5.4 Implementation of the Direct Inverse Radon Transform 176
5.5 LinogramMethod 179
5.6 Simple Backprojection 184
5.7 Filtered Backprojection 188
5.8 Comparison Between Backprojection and Filtered Backprojection 192
5.9 Filtered Layergram: Deconvolution of the Simple Backprojection 196
5.10 Filtered Backprojection and Radon’s Solution 200
5.11 Cormack Transform 203
6 Algebraic and Statistical ReconstructionMethods 210
6.1 Introduction 210
6.2 Solution with Singular Value Decomposition 216
6.3 Iterative Reconstruction with ART 220
6.4 Pixel Basis Functions and Calculation of the SystemMatrix 227
6.5 Maximum Likelihood Method 232
7 Technical Implementation 250
7.1 Introduction 250
7.2 Reconstruction with Real Signals 251
7.3 Practical Implementation of the Filtered Backprojection 264
7.4 Minimum Number of Detector Elements 267
7.5 Minimum Number of Projections 268
7.6 Geometry of the Fan-Beam System 270
7.7 Image Reconstruction for Fan-Beam Geometry 271
7.8 Quarter-Detector Offset and Sampling Theorem 302
8 Three-Dimensional Fourier-Based ReconstructionMethods 311
8.1 Introduction 311
8.2 Secondary Reconstruction Based on 2D Stacks of Tomographic Slices 312
8.3 Spiral CT 317
8.4 Exact 3D Reconstruction in Parallel-Beam Geometry 329
8.5 Exact 3D Reconstruction in Cone-Beam Geometry 344
8.6 Approximate 3D Reconstructions in Cone-BeamGeometry 374
8.7 Helical Cone-Beam Reconstruction Methods 402
9 Image Quality and Artifacts 410
9.1 Introduction 410
9.2 Modulation Transfer Function of the Imaging Process 411
9.3 Modulation Transfer Function and Point Spread Function 417
9.4 Modulation Transfer Function in Computed Tomography 419
9.5 SNR, DQE, and ROC 428
9.6 2D Artifacts 430
9.7 3D Artifacts 452
9.8 Noise in Reconstructed Images 469
10 Practical Aspects of Computed Tomography 477
10.1 Introduction 477
10.2 Scan Planning 477
10.3 Data Representation 481
10.4 Some Applications in Medicine 488
11 Dose 491
11.1 Introduction 491
11.2 Energy Dose, Equivalent Dose, and Effective Dose 492
11.3 Definition of Specific CT Dose Measures 493
11.4 Device-Related Measures for Dose Reduction 499
11.5 User-Related Measures for Dose Reduction 505
References 509
Subject Index 516

Produkt-Details

• Erscheint lt. Verlag: 20.5.2008
• Zusatzinfo: XIV, 522 p. 475 illus., 296 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Medizin / Pharmazie ► Medizinische Fachgebiete
• Themenwelt: Studium ► 2. Studienabschnitt (Klinik) ► Anamnese / Körperliche Untersuchung
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Schlagworte: biomedical engineering • Computed tomography (CT) • Cone-beam Reconstruction • CT Dose • CT Reconstruction Methods • Imaging Artefacts • medical physics • Tomography • X-Ray • X-ray Tubes and Detectors
• ISBN-10: 3-540-39408-7 / 3540394087
• ISBN-13: 978-3-540-39408-2 / 9783540394082