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vii | |
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xi | |
Foreword |
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xiii | |
Preface |
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xiv | |
Acknowledgements |
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xvi | |
Color Plates |
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xvii | |
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1 Mathematical Techniques |
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3 | (7) |
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3 | (4) |
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1.1.2 Group-sparse Recovery |
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7 | (1) |
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1.1.3 Row-sparse Multiple Measurement Vector Recovery |
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8 | (1) |
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1.1.4 Synthesis and Analysis Priors |
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9 | (1) |
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1.2 Low-rank Matrix Recovery |
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10 | (3) |
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13 | (2) |
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15 | (15) |
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15 | (6) |
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21 | (9) |
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1.5 Split Bregman Techniques |
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30 | (7) |
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1.5.1 Multiple Penalty Problems |
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34 | (3) |
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37 | (13) |
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Appendix: Greedy Algorithms |
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38 | (6) |
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44 | (6) |
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2 Single Channel Static MR Image Reconstruction |
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2.1 Single Echo MRI Reconstruction |
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50 | (22) |
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52 | (3) |
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55 | (3) |
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2.1.3 Reconstruction Algorithms |
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58 | (4) |
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2.1.4 Engineering the Measurement Operator |
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62 | (3) |
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2.1.5 Structured Sparsity |
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65 | (7) |
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72 | (15) |
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2.2.1 Physics of MR Image Contrast |
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73 | (2) |
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2.2.2 Group-Sparse Reconstruction of Multi-echo MRI |
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75 | (6) |
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Appendix: Mixed Prior Optimization |
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81 | (3) |
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84 | (3) |
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3 Multi-Coil Parallel MRI Reconstruction |
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3.1 Frequency Domain Methods |
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87 | (11) |
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88 | (1) |
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89 | (1) |
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90 | (2) |
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92 | (2) |
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3.1.5 Extensions to GRAPPA |
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94 | (4) |
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98 | (9) |
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3.2.1 SENSitivity Encoding |
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99 | (1) |
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100 | (3) |
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103 | (1) |
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104 | (3) |
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3.3 Calibration-Free Reconstruction |
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107 | (9) |
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3.3.1 Calibration-Less Multi-coil MRI |
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109 | (7) |
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116 | (5) |
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117 | (4) |
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4 Dynamic MRI Reconstruction |
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4.1 Offline Dynamic MRI Reconstruction |
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121 | (19) |
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4.1.1 Compressed Sensing-Based Reconstruction Techniques |
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121 | (4) |
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4.1.2 Low-Rank Methods in Dynamic MRI Reconstruction |
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125 | (2) |
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4.1.3 Combined Low-Rank and Sparsity-Based Techniques |
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127 | (10) |
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4.1.4 Sparse + Low-Rank Reconstruction |
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137 | (3) |
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4.2 Online Reconstruction |
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140 | (13) |
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4.2.1 Compressed Sensing-Based Techniques |
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140 | (6) |
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4.2.2 Kalman Filter-Based Techniques |
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146 | (3) |
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149 | (4) |
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153 | (3) |
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4.3.1 Image Domain Methods |
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153 | (3) |
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156 | (4) |
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157 | (3) |
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5 Applications in Other Areas |
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160 | (12) |
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5.1.1 Compressed Sensing in Static CT Reconstruction |
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162 | (5) |
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5.1.2 Compressed Sensing in Dynamic CT |
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167 | (5) |
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5.2 Diffusion Tensor Imaging |
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172 | (5) |
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5.2.1 Distributed Compressed Sensing |
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173 | (1) |
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5.2.2 Learned Dictionary Approach |
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174 | (1) |
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5.2.3 Direct Diffusivity Estimation |
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175 | (2) |
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5.3 Compressed Sensing in EEG Reconstruction |
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177 | (12) |
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5.3.1 Improving Transmission Energy Efficiency by Compressed Sensing |
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177 | (7) |
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5.3.2 Improving Sensing Energy Efficiency |
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184 | (5) |
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189 | (5) |
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190 | (4) |
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194 | (7) |
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6.1.1 Recursive Least Squares |
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197 | (1) |
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6.1.2 Recursive l1-Filtering |
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198 | (3) |
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201 | (1) |
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201 | (3) |
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6.2.1 Non-linear Compressed Sensing Recovery |
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202 | (2) |
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6.3 Parallelizing MRI Reconstruction Algorithms |
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204 | (3) |
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205 | (2) |
Index |
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207 | (1) |
About the author |
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208 | |