Principles of magnetic resonance imaging: a signal processing perspective
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
IEEE Press [u.a.]
2000
|
| Series: | IEEE Press series in biomedical engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 416 S. Ill., graph. Darst. |
| ISBN: | 0780347234 0819435163 |
Staff View
MARC
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| 245 | 1 | 0 | |a Principles of magnetic resonance imaging |b a signal processing perspective |c Zhi-Pei Liang ; Paul C. Lauterbur |
| 264 | 1 | |a New York |b IEEE Press [u.a.] |c 2000 | |
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Record in the Search Index
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| adam_text | Contents
Preface xiii
Acknowledgments xv
1 Introduction 1
1.1 WhatlsMRI? 2
1.2 A System Perspective 5
1.2.1 The Main Magnet 5
1.2.2 The Gradient System 6
1.2.3 The RF System 7
1.3 A Signal Processing Perspective 7
1.4 Organization of the Book 9
Exercises 11
2 Mathematical Fundamentals 13
2.1 Vectors 13
2.2 Basic Concepts of Matrix Algebra 17
2.3 Some Commonly Used Functions 19
2.3.1 Unit Step Function 19
2.3.2 Signum Function 19
2.3.3 Rectangular Window Function 19
2.3.4 Triangle Window Function 19
2.3.5 Hamming Window Function 19
2.3.6 Gaussian Function 20
2.3.7 Dirac Delta Function 20
2.3.8 Kronecker Delta Function 22
2.3.9 Comb Function 22
2.3.10 Sine Function 23
2.3.11 Dirichlet Function 23
2.3.12 Bessel Functions 24
2.4 Convolution 26
2.5 The Fourier Transform 28
vii
2.5.1 Definition 29
2.5.2 Properties 30
2.5.3 Examples 32
2.6 The Radon Transform 36
2.6.1 Two Dimensional Radon Transforms 36
2.6.2 Higher Dimensional Radon Transforms 38
2.6.3 Partial Radon Transforms 40
2.6.4 Basic Properties 43
2.6.5 Sinogram 43
2.6.6 The Projection Slice Theorem 45
2.6.7 Convolution Theorem 50
Exercises 52
3 Signal Generation and Detection 57
3.1 Magnetized Nuclear Spin Systems 58
3.1.1 Nuclear Magnetic Moments 58
3.1.2 Bulk Magnetization 64
3.1.3 More on the Larmor Frequency 68
3.2 RF Excitations 69
3.2.1 Resonance Condition 69
3.2.2 Characteristics of an RF Pulse 70
3.2.3 Rotating Frame of Reference 72
3.2.4 The Bloch Equation 76
3.2.5 On Resonance Excitations 77
3.2.6 Off Resonance Excitations 87
3.2.7 Frequency Selectivity of an RF Pulse 88
3.3 Free Precession and Relaxation 91
3.4 Signal Detection 94
3.4.1 Basic Detection Principles 94
3.4.2 Signal Expressions 95
Exercises 101
4 Signal Characteristics 107
4.1 Basic Assumptions 107
4.2 Free Induction Decays 109
4.3 RF Echoes 114
4.3.1 Two Pulse Echo 114
4.3.2 Three Pulse Echoes 120
4.3.3 Extended Phase Graphs 125
4.3.4 The CPMG Echo Train 130
4.4 Gradient Echoes 131
4.4.1 Gradient Fields 131
4.4.2 Formation of Gradient Echoes 133
Exercises 136
5 Signal Localization 141
5.1 Slice Selection 142
5.1.1 Slice Equation 142
5.1.2 Slice Selective Gradients 143
5.1.3 Slice Selective RF Pulses 145
5.1.4 Some Practical Considerations 149
5.2 Spatial Information Encoding 153
5.2.1 Frequency Encoding 153
5.2.2 Phase Encoding 155
5.2.3 A fc Space Interpretation 157
5.3 Basic Imaging Methods 165
5.3.1 One Dimensional Imaging 165
5.3.2 Two Dimensional Imaging 167
5.3.3 Three Dimensional Imaging 171
5.4 Sampling of fc Space 173
5.4.1 The Sampling Theorem 173
5.4.2 Sampling Requirements of fc Space Signals 176
Exercises 180
6 Image Reconstruction 187
6.1 General Issues of Image Reconstruction 188
6.2 Reconstruction from Fourier Transform Samples 190
6.2.1 Problem Formulation 190
6.2.2 Basic Theory 190
6.2.3 Computational Algorithms 195
6.3 Reconstruction from Radon Transform Samples 199
6.3.1 Problem Formulation 199
6.3.2 The Inverse Radon Transform 200
6.3.3 Backprojection 202
6.3.4 Practical Reconstruction Algorithms 204
6.4 Appendix 213
Exercises 214
7 Image Contrast 217
7.1 Introduction 217
7.2 Saturation Recovery Sequence 218
7.3 Inversion Recovery Sequence 221
7.4 Basic Spin Echo Imaging 223
7.5 Basic Gradient Echo Imaging 225
7.6 Discussion 227
Exercises 230
8 Image Resolution, Noise, and Artifacts 233
8.1 Resolution Limitations 233
8.1.1 Point Spread Function 233
8.1.2 PSF of Fourier Reconstructions 235
8.1.3 PSF of Backprojection Reconstructions 237
8.2 Image Noise 239
8.2.1 Basic Concepts of Random Signals 239
8.2.2 Noise Characteristics in the Data Domain 245
8.2.3 Noise in Direct FFT Reconstruction 246
8.2.4 Noise in Zero Padded FFT Reconstruction 248
8.2.5 Noise in Filtered Backprojection Reconstruction 250
8.3 Image Artifacts 251
8.3.1 Gibbs Ringing Artifact 251
8.3.2 Aliasing Artifacts 255
8.3.3 Chemical Shift Artifact 258
8.3.4 Motion Artifacts 260
8.3.5 Artifacts Due to Corrupted Data 281
Exercises 285
9 Fast Scan Imaging 291
9.1 Fast Spin Echo Imaging 291
9.1.1 Basic Concept 292
9.1.2 Practical Issues 295
9.2 Fast Gradient Echo Imaging 297
9.2.1 Spoiled Steady State Imaging 297
9.2.2 Steady State Imaging 300
9.3 Echo Planar Imaging 303
9.3.1 Zigzag Trajectory 304
9.3.2 Rectilinear Trajectory 307
9.3.3 Spiral Trajectory 308
9.3.4 Discussion 311
9.4 Burst Imaging 311
Exercises 315
10 Constrained Reconstruction 321
10.1 Half Fourier Reconstruction 322
10.1.1 Phase Estimation 323
10.1.2 Phase Constrained Reconstruction 323
10.1.3 Discussion 327
10.2 Extrapolation Based Reconstruction 331
10.2.1 Bandlimited Extrapolation 332
10.2.2 Maximum Entropy Reconstruction 334
10.2.3 Discussion 337
10.3 Parametric Reconstruction Methods 339
10.3.1 The Autoregressive Moving Average Model 340
10.3.2 The Generalized Series Model 347
10.4 Appendix 355
10.4.1 The Direct Least Squares Method 356
10.4.2 SVD Based Methods 357
Exercises 363
A Mathematical Formulas 367
A.I Sums 367
A.2 Power Series 367
A.3 Complex Numbers 368
A.4 Trigonometric Identities 368
A.5 Short Tables of Convolutions 369
A.6 A Short Table of Fourier Transforms 370
B Glossary 371
C Abbreviations 383
D Mathematical Symbols 385
£ Physical Constants 389
Bibliography 391
Index 409
About the Authors 415
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| spelling | Liang, Zhi-Pei 1961- Verfasser (DE-588)173356680 aut Principles of magnetic resonance imaging a signal processing perspective Zhi-Pei Liang ; Paul C. Lauterbur New York IEEE Press [u.a.] 2000 xv, 416 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier IEEE Press series in biomedical engineering NMR-Bildgebung Magnetic resonance imaging Congresses Nuclear magnetic resonance Congresses Signal processing Congresses Kernspintomografie (DE-588)4120806-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Kernspintomografie (DE-588)4120806-7 s DE-604 Lauterbur, Paul C. 1929-2007 Verfasser (DE-588)13281191X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008552193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liang, Zhi-Pei 1961- Lauterbur, Paul C. 1929-2007 Principles of magnetic resonance imaging a signal processing perspective NMR-Bildgebung Magnetic resonance imaging Congresses Nuclear magnetic resonance Congresses Signal processing Congresses Kernspintomografie (DE-588)4120806-7 gnd |
| subject_GND | (DE-588)4120806-7 (DE-588)1071861417 |
| title | Principles of magnetic resonance imaging a signal processing perspective |
| title_auth | Principles of magnetic resonance imaging a signal processing perspective |
| title_exact_search | Principles of magnetic resonance imaging a signal processing perspective |
| title_full | Principles of magnetic resonance imaging a signal processing perspective Zhi-Pei Liang ; Paul C. Lauterbur |
| title_fullStr | Principles of magnetic resonance imaging a signal processing perspective Zhi-Pei Liang ; Paul C. Lauterbur |
| title_full_unstemmed | Principles of magnetic resonance imaging a signal processing perspective Zhi-Pei Liang ; Paul C. Lauterbur |
| title_short | Principles of magnetic resonance imaging |
| title_sort | principles of magnetic resonance imaging a signal processing perspective |
| title_sub | a signal processing perspective |
| topic | NMR-Bildgebung Magnetic resonance imaging Congresses Nuclear magnetic resonance Congresses Signal processing Congresses Kernspintomografie (DE-588)4120806-7 gnd |
| topic_facet | NMR-Bildgebung Magnetic resonance imaging Congresses Nuclear magnetic resonance Congresses Signal processing Congresses Kernspintomografie Konferenzschrift |
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