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E-grāmata: Compressed Sensing for Magnetic Resonance Image Reconstruction

  • Formāts: PDF+DRM
  • Izdošanas datums: 26-Feb-2015
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781316674284
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Compressed Sensing for Magnetic Resonance Image ReconstructionPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 26-Feb-2015
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781316674284
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Expecting the reader to have some basic training in liner algebra and optimization, the book begins with a general discussion on CS techniques and algorithms. It moves on to discussing single channel static MRI, the most common modality in clinical studies. It then takes up multi-channel MRI and the interesting challenges consequently thrown up in signal reconstruction. Off-line and on-line techniques in dynamic MRI reconstruction are visited. Towards the end the book broadens the subject by discussing how CS is being applied to other areas of biomedical signal processing like X-ray, CT and EEG acquisition. The emphasis throughout is on qualitative understanding of the subject rather than on quantitative aspects of mathematical forms. The book is intended for MRI engineers interested in the brass tacks of image formation; medical physicists interested in advanced techniques in image reconstruction; and mathematicians or signal processing engineers.

Papildus informācija

This book discusses different ways to use the existing mathematical techniques to solve problems in compressed sensing.
List of Figures
vii
List of Tables
xi
Foreword xiii
Preface xiv
Acknowledgements xvi
Color Plates xvii
1 Mathematical Techniques
1.1 Compressed Sensing
3(7)
1.1.1 Sparse Recovery
3(4)
1.1.2 Group-sparse Recovery
7(1)
1.1.3 Row-sparse Multiple Measurement Vector Recovery
8(1)
1.1.4 Synthesis and Analysis Priors
9(1)
1.2 Low-rank Matrix Recovery
10(3)
1.3 Kalman Filter
13(2)
1.4 Algorithms
15(15)
1.4.1 Noiseless Scenario
15(6)
1.4.2 Noisy Scenario
21(9)
1.5 Split Bregman Techniques
30(7)
1.5.1 Multiple Penalty Problems
34(3)
1.6 Conclusion
37(13)
Appendix: Greedy Algorithms
38(6)
References
44(6)
2 Single Channel Static MR Image Reconstruction
2.1 Single Echo MRI Reconstruction
50(22)
2.1.1 Sparsity
52(3)
2.1.2 Incoherence
55(3)
2.1.3 Reconstruction Algorithms
58(4)
2.1.4 Engineering the Measurement Operator
62(3)
2.1.5 Structured Sparsity
65(7)
2.2 Multi-echo MRI
72(15)
2.2.1 Physics of MR Image Contrast
73(2)
2.2.2 Group-Sparse Reconstruction of Multi-echo MRI
75(6)
Appendix: Mixed Prior Optimization
81(3)
References
84(3)
3 Multi-Coil Parallel MRI Reconstruction
3.1 Frequency Domain Methods
87(11)
3.1.1 GRAPPA
88(1)
3.1.2 Regularized GRAPPA
89(1)
3.1.3 Iterative GRAPPA
90(2)
3.1.4 Kernel GRAPPA
92(2)
3.1.5 Extensions to GRAPPA
94(4)
3.2 Image Domain Methods
98(9)
3.2.1 SENSitivity Encoding
99(1)
3.2.2 Regularized SENSE
100(3)
3.2.3 CS SENSE
103(1)
3.2.4 Iterative SENSE
104(3)
3.3 Calibration-Free Reconstruction
107(9)
3.3.1 Calibration-Less Multi-coil MRI
109(7)
3.4 Conclusion
116(5)
References
117(4)
4 Dynamic MRI Reconstruction
4.1 Offline Dynamic MRI Reconstruction
121(19)
4.1.1 Compressed Sensing-Based Reconstruction Techniques
121(4)
4.1.2 Low-Rank Methods in Dynamic MRI Reconstruction
125(2)
4.1.3 Combined Low-Rank and Sparsity-Based Techniques
127(10)
4.1.4 Sparse + Low-Rank Reconstruction
137(3)
4.2 Online Reconstruction
140(13)
4.2.1 Compressed Sensing-Based Techniques
140(6)
4.2.2 Kalman Filter-Based Techniques
146(3)
4.2.3 Hybrid Methods
149(4)
4.3 Dynamic Parallel MRI
153(3)
4.3.1 Image Domain Methods
153(3)
4.4 Conclusion
156(4)
References
157(3)
5 Applications in Other Areas
5.1 Computer Tomography
160(12)
5.1.1 Compressed Sensing in Static CT Reconstruction
162(5)
5.1.2 Compressed Sensing in Dynamic CT
167(5)
5.2 Diffusion Tensor Imaging
172(5)
5.2.1 Distributed Compressed Sensing
173(1)
5.2.2 Learned Dictionary Approach
174(1)
5.2.3 Direct Diffusivity Estimation
175(2)
5.3 Compressed Sensing in EEG Reconstruction
177(12)
5.3.1 Improving Transmission Energy Efficiency by Compressed Sensing
177(7)
5.3.2 Improving Sensing Energy Efficiency
184(5)
5.4 Conclusion
189(5)
References
190(4)
6 Some Open Problems
6.1 Interactive Sampling
194(7)
6.1.1 Recursive Least Squares
197(1)
6.1.2 Recursive l1-Filtering
198(3)
6.1.3 Discussion
201(1)
6.2 Quantitative MRI
201(3)
6.2.1 Non-linear Compressed Sensing Recovery
202(2)
6.3 Parallelizing MRI Reconstruction Algorithms
204(3)
References
205(2)
Index 207(1)
About the author 208
Angshul Majumdar completed his Master's and PhD at the University of British Columbia in 2009 and 2012 respectively. He is currently Assistant Professor at Indraprastha Institute of Information Technology, New Delhi. His primary research interests are optimization algorithms for sparse vector recovery and low-rank matrix completion. The application areas of his research spans across medical imaging, biomedical signal processing, radar signal processing and collaborative filtering recommender systems.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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