Preface |
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vii | |
Editor |
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xi | |
Contributors |
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xiii | |
1 Compressive Sensing Fundamentals |
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1 | (48) |
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2 | (5) |
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1.1.1 Signal Models and Dimensionality Reduction |
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2 | (1) |
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1.1.2 Motivation for Compressive Sensing |
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3 | (2) |
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1.1.3 Compressive Sensing in a Nutshell |
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5 | (2) |
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7 | (8) |
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1.2.1 Sparsity, Compressibility, and Norms |
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7 | (1) |
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1.2.2 Sparsity in Orthonormal Bases |
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8 | (2) |
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1.2.3 Sparsity in Nonorthonormal Dictionaries |
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10 | (2) |
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1.2.3.1 Synthesis Sparsity |
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10 | (1) |
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1.2.3.2 Analysis Sparsity |
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11 | (1) |
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1.2.4 Extensions of Sparse Models |
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12 | (3) |
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1.2.4.1 Structured Sparsity Models |
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12 | (1) |
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1.2.4.2 Statistical Sparsity Models |
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13 | (1) |
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14 | (1) |
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1.3 Compressive Measurement Protocols |
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15 | (9) |
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1.3.1 Random Gaussian and Subgaussian Matrices |
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16 | (3) |
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1.3.2 Random Sampling in an Orthogonal Basis |
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19 | (1) |
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1.3.3 Measurement Systems |
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20 | (4) |
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1.3.3.1 One-Dimensional Signals |
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21 | (1) |
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1.3.3.2 Images and Higher-Dimensional Signals |
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22 | (2) |
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1.4 Sparse Signal Recovery Algorithms and Guarantees |
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24 | (12) |
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24 | (2) |
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1.4.2 Optimization-Based Recovery from Noise-Free Measurements |
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26 | (2) |
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1.4.2.1 Problem Formulation |
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26 | (1) |
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1.4.2.2 Performance Guarantees |
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26 | (2) |
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1.4.2.3 Computational Considerations |
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28 | (1) |
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1.4.3 Optimization-Based Recovery from Noisy Measurements |
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28 | (2) |
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1.4.3.1 Problem Formulation |
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28 | (1) |
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1.4.3.2 Performance Guarantees |
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29 | (1) |
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1.4.3.3 Computational Considerations |
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29 | (1) |
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1.4.3.4 Parameter Selection |
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30 | (1) |
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30 | (4) |
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1.4.4.1 Orthogonal Matching Pursuit (OMP) |
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30 | (2) |
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1.4.4.2 Compressive Sampling Matching Pursuit (CoSaMP) |
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32 | (1) |
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1.4.4.3 Iterative Hard Thresholding (IHT) |
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33 | (1) |
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1.4.5 Signal Recovery in Nonorthonormal Dictionaries |
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34 | (16) |
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1.4.5.1 Synthesis Sparsity in Redundant Dictionaries |
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34 | (1) |
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1.4.5.2 Analysis Sparsity |
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35 | (1) |
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36 | (1) |
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37 | (12) |
2 Overcomplete Dictionary Design for Building Feature Extraction |
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49 | (38) |
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50 | (5) |
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2.1.1 Overview of Through-Wall Radar Mapping |
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50 | (2) |
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2.1.2 Typical Measurement Geometry |
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52 | (1) |
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2.1.3 Bases, Frames, and Overcomplete Dictionaries |
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52 | (3) |
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2.1.4 Layout of This Chapter |
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55 | (1) |
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2.2 Building Feature Extraction |
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55 | (4) |
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2.2.1 Point Scattering Focusing |
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55 | (2) |
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2.2.2 Smashed Filter Processing |
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57 | (1) |
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2.2.3 OCD with Sparse Representation |
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58 | (1) |
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59 | (3) |
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2.3.1 Knowledge-Based Dictionaries |
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59 | (1) |
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2.3.2 Adaptive Knowledge-Based Dictionaries |
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60 | (1) |
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61 | (1) |
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2.4 Practical Atom Definition |
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62 | (7) |
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62 | (3) |
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65 | (4) |
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2.5 Through-Wall Radar Measurements |
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69 | (13) |
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70 | (1) |
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2.5.2 Point Scattering Focusing |
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71 | (3) |
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2.5.2.1 Reflectivity Maps |
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71 | (1) |
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2.5.2.2 Classified Scatterers |
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72 | (2) |
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2.5.3 Smashed Filter Processing |
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74 | (4) |
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2.5.3.1 Reflectivity Maps |
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74 | (2) |
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2.5.3.2 Classified Scatterers |
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76 | (2) |
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2.5.4 OCD with Sparse Representation |
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78 | (16) |
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79 | (1) |
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2.5.4.2 Reflectivity Maps |
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80 | (1) |
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2.5.4.3 Classified Scatterers |
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80 | (2) |
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82 | (2) |
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84 | (3) |
3 Compressive Sensing for Radar Imaging of Underground Targets |
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87 | (36) |
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88 | (2) |
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3.2 Background for GPR Imaging |
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90 | (4) |
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3.3 System Framework with CS |
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94 | (11) |
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95 | (4) |
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96 | (2) |
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3.3.1.2 Stepped Frequency Phi |
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98 | (1) |
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99 | (2) |
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3.3.3 Compressed Orthogonal Matching Pursuit |
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101 | (1) |
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3.3.4 Basic CS Simulation |
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102 | (3) |
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3.4 Computational Reductions |
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105 | (10) |
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3.4.1 Shift Invariance Property |
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106 | (4) |
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3.4.2 Implementation Specifics for Structure Change |
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110 | (3) |
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3.4.3 Simulation Using Functional Dictionary |
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113 | (2) |
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3.5 Applied Performance: Laboratory Data |
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115 | (4) |
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3.5.1 Air-Target Experiment |
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116 | (1) |
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3.5.2 Subsurface-Target Experiment |
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117 | (2) |
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119 | (1) |
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119 | (4) |
4 Wall Clutter Mitigations for Compressive Imaging of Building Interiors |
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123 | (30) |
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124 | (3) |
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4.2 Wall Mitigation Techniques of Spatial Filtering and Subspace Projection |
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127 | (5) |
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4.2.1 Through-the-Wall Signal Model |
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127 | (2) |
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4.2.2 Wall Clutter Mitigation Techniques |
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129 | (2) |
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4.2.2.1 Spatial Filtering |
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129 | (1) |
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4.2.2.2 Subspace Projection |
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130 | (1) |
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4.2.3 Scene Reconstruction |
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131 | (1) |
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4.2.4 Illustrative Results |
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132 | (1) |
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4.3 Spatial Filtering and Subspace Projection under Reduced Data Volume |
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132 | (4) |
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4.3.1 Wall Mitigations under Reduced Data Volume |
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134 | (1) |
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4.3.2 CS-Based Scene Reconstruction |
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134 | (1) |
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4.3.3 Illustrative Results |
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135 | (1) |
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4.4 Wall Clutter Mitigation Using DPSSs |
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136 | (5) |
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4.4.1 Discrete Prolate Spheroidal Sequences |
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137 | (1) |
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137 | (2) |
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4.4.3 Block-Sparse Reconstruction |
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139 | (1) |
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4.4.4 Illustrative Results |
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140 | (1) |
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4.5 Partially Sparse Reconstruction of Indoor Scenes |
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141 | (7) |
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4.5.1 Partially Sparse Signal Model |
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142 | (2) |
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4.5.2 Sparse Scene Reconstruction |
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144 | (1) |
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4.5.3 Illustrative Results |
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145 | (3) |
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148 | (1) |
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148 | (5) |
5 Compressive Sensing for Urban Multipath Exploitation |
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153 | (44) |
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154 | (1) |
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5.2 Ultrawideband Signal Model |
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155 | (5) |
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5.2.1 Relation to the Stationary Scene Model |
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158 | (1) |
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5.2.2 Conventional Image Formation |
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159 | (1) |
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5.3 Multipath Propagation Model |
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160 | (10) |
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5.3.1 Interior Wall Multipath |
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162 | (1) |
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5.3.2 Wall Ringing Multipath |
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163 | (2) |
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5.3.3 Bistatic Received Signal Model |
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165 | (5) |
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5.4 Compressive Sensing Reconstruction with Multipath Exploitation |
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170 | (7) |
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170 | (1) |
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5.4.2 Group Sparse Reconstruction of Stationary Scenes |
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170 | (3) |
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173 | (4) |
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5.4.3.1 Simulation Results |
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174 | (1) |
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5.4.3.2 Experimental Results |
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175 | (2) |
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177 | (5) |
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5.4.5 Group Sparse Reconstruction of Stationary/Nonstationary Scenes |
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178 | (1) |
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179 | (3) |
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5.4.6.1 Simulation Results |
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179 | (2) |
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5.4.6.2 Experimental Results |
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181 | (1) |
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5.5 Compressive Sensing Reconstruction with the Wall Included |
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182 | (8) |
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5.5.1 Wall Reverberation Model |
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184 | (2) |
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5.5.2 Separate Reconstruction |
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186 | (1) |
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5.5.3 Joint Group Sparse Reconstruction |
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186 | (2) |
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188 | (12) |
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5.5.4.1 Simulation Results |
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188 | (2) |
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5.5.4.2 Experimental Results |
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190 | (1) |
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190 | (2) |
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192 | (1) |
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192 | (5) |
6 Measurement Kernel Design for HRR Imaging of Urban Objects |
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197 | (34) |
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198 | (2) |
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6.2 Sub-Nyquist Sampling Implementations, Models, and Constraints |
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200 | (8) |
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6.2.1 Implementation of Sub-Nyquist Sampling |
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201 | (2) |
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6.2.2 Power and Cost Benefits |
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203 | (1) |
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6.2.3 Measurement Model with Preprojection Additive Noise |
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204 | (2) |
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6.2.4 Matrix-Vector Measurement Model |
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206 | (2) |
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6.3 Radar Target and Received Signal Models |
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208 | (3) |
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6.3.1 Linear Target Model |
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208 | (3) |
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211 | (1) |
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6.3.3 Signal-to-Noise Ratio |
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211 | (1) |
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6.4 Information-Based Measurement Kernel Optimization |
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211 | (8) |
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6.4.1 Task-Specific Information |
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212 | (1) |
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6.4.2 Approximate Gradient of TSI for a Gaussian Mixture Model |
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213 | (4) |
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6.4.3 Application to HRR Imaging |
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217 | (2) |
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6.4.4 MMSE HRR Estimation |
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219 | (1) |
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219 | (8) |
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6.5.1 Training Data and Gaussian Mixture Calculation |
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219 | (1) |
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6.5.2 Waveforms and Compression Ratio |
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220 | (1) |
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221 | (2) |
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6.5.4 Quantitative Performance Results |
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223 | (4) |
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227 | (1) |
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228 | (1) |
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228 | (3) |
7 Compressive Sensing for Multipolarization through-the-Wall Radar Imaging |
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231 | (20) |
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232 | (1) |
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7.2 Through-the-Wall Radar Imaging |
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233 | (5) |
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7.2.1 Delay-and-Sum Beamforming |
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233 | (2) |
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7.2.2 Single-Polarization Imaging Using SMV Model |
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235 | (2) |
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7.2.3 Multipolarization Imaging Using SMV Model |
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237 | (1) |
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7.3 Multipolarization Imaging Using MMV Model |
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238 | (2) |
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238 | (1) |
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7.3.2 Joint Image Fusion and Formation Using MMV |
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238 | (2) |
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240 | (6) |
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7.4.1 Experimental Results Using Synthetic Data |
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241 | (2) |
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7.4.2 Experimental Results Using Real Data |
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243 | (3) |
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246 | (2) |
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248 | (3) |
8 Sparsity-Aware Human Motion Indication |
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251 | (32) |
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252 | (2) |
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254 | (13) |
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8.2.1 Backprojection-Based Change Detection |
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254 | (2) |
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8.2.2 Sparsity-Driven Change Detection under Translational Motion |
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256 | (2) |
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8.2.3 Sparsity-Driven Change Detection under Short Sudden Movements |
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258 | (4) |
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8.2.4 Experimental Results for Change Detection |
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262 | (5) |
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8.3 Sparsity for Target Localization and Motion Parameter Estimation |
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267 | (10) |
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268 | (3) |
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8.3.2 Backprojection-Based Stationary and Moving Target Localization |
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271 | (2) |
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8.3.3 CS-Based Stationary and Moving Target Localization |
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273 | (3) |
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8.3.3.1 Linear Model Formulation |
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273 | (1) |
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8.3.3.2 CS Data Acquisition and Scene Reconstruction |
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274 | (2) |
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8.3.4 Experimental Results |
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276 | (1) |
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277 | (2) |
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279 | (4) |
9 Time-Frequency Analysis of Micro-Doppler Signals Based on Compressive Sensing |
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283 | (44) |
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284 | (2) |
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286 | (3) |
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9.2.1 Time-Varying Micro-Doppler Signatures |
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286 | (3) |
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9.2.2 Human Gait Modeling |
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289 | (1) |
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9.3 Time-Frequency Analysis of the m-D and Rigid Body Signals |
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289 | (6) |
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9.3.1 Missing STFT Samples due to the m-D Removal |
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291 | (4) |
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9.4 Sparse Compressive Sensed Signals and Time-Frequency Analysis |
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295 | (10) |
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9.4.1 Missing Samples due to Reduced Sampling Rate |
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295 | (3) |
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9.4.2 Analysis of Missing Samples in the FT (STFT) Domain |
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298 | (4) |
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9.4.3 Effects of Missing Samples to Bilinear Time-Frequency Distributions |
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302 | (3) |
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9.5 CS Reconstructions in Time-Frequency Domain |
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305 | (18) |
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9.5.1 Signal Reconstruction from Bilinear Transforms |
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305 | (6) |
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9.5.1.1 Ambiguity Domain-Based CS |
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305 | (2) |
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9.5.1.2 IAF Reconstruction Yielding Sparse TFR |
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307 | (1) |
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9.5.1.3 Robust Ambiguity Domain-Based CS in the Presence of Impulse Noise |
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308 | (3) |
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9.5.2 Compressive Sensing Reconstruction from Linear Transforms |
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311 | (7) |
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9.5.2.1 Reconstruction Based on the CS Methods |
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314 | (4) |
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9.5.3 Windows with Overlapping |
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318 | (5) |
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323 | (1) |
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324 | (3) |
10 Urban Target Tracking Using Sparse Representations |
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327 | (34) |
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328 | (2) |
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330 | (6) |
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10.2.1 Multipath Environment Model |
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330 | (4) |
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334 | (1) |
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335 | (1) |
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336 | (1) |
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336 | (6) |
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10.4 Sparsity-Based Multiple-Target Tracking |
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342 | (9) |
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10.4.1 Standard Sparse Signal Reconstruction Techniques |
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343 | (1) |
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10.4.2 Effect of Multipath Environment |
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344 | (5) |
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10.4.3 PB Support Recovery Algorithm |
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349 | (2) |
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351 | (3) |
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354 | (2) |
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356 | (5) |
11 Three-Dimensional Imaging of Vehicles from Sparse Apertures in Urban Environment |
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361 | (26) |
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362 | (1) |
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363 | (4) |
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11.3 Case Study for 3-D SAR: AFRL GOTCHA Volumetric SAR Data Set |
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367 | (2) |
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11.4 Direct Approach to Sparsity-Regularized 3-D Construction |
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369 | (4) |
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11.4.1 Algorithmic and Computational Considerations |
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371 | (2) |
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11.5 Multiple Elevation IFSAR |
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373 | (8) |
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11.5.1 Sparsity-Regularized Interpolation Approach to m-IFSAR |
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376 | (3) |
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11.5.2 DFT Peak Detection Approach for m-IFSAR |
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379 | (2) |
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11.6 Practical Considerations: Autofocus and Registration |
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381 | (2) |
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383 | (4) |
12 Compressive Sensing for MIMO Urban Radar |
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387 | (42) |
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388 | (1) |
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12.1.1 Outline of the Chapter |
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389 | (1) |
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12.2 Colocated CS-MIMO Radars |
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389 | (8) |
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12.2.1 Problem Formulation and Solution |
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389 | (8) |
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12.3 Challenging Issues Associated with CS-MIMO Radars |
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397 | (7) |
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12.3.1 Basis Mismatch and Resolution |
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398 | (1) |
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398 | (1) |
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12.3.3 Clutter Rejection: CS-Capon |
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398 | (6) |
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12.3.4 Phase Synchronization |
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404 | (1) |
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12.4 Advanced Techniques for CS-MIMO Radars |
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404 | (14) |
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404 | (7) |
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12.4.2 Waveform Design for Colocated CS-MIMO Radars |
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411 | (1) |
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12.4.3 Measurement Matrix Design |
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412 | (18) |
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12.4.3.1 Measurement Matrix Design by Reducing CSM and Increasing SIR |
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413 | (2) |
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12.4.3.2 Measurement Matrix Design by Improving SIR Only |
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415 | (2) |
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12.4.3.3 Phi#1 versus Phi#2 |
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417 | (1) |
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12.5 Application to Through-the-Wall Radar |
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418 | (6) |
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424 | (1) |
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424 | (5) |
13 Compressive Sensing Meets Noise Radar |
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429 | (32) |
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430 | (5) |
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13.1.1 State of the Art in Compressive Radar Imaging |
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433 | (2) |
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13.2 Basics of Compressive Stochastic Waveform Radar |
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435 | (7) |
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435 | (2) |
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13.2.2 Correlations in the Circulant Matrix |
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437 | (1) |
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437 | (2) |
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13.2.4 Analysis of Experimental Data |
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439 | (1) |
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13.2.5 Imaging Performance |
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439 | (3) |
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13.3 Detection Strategies for Compressive Noise Radar |
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442 | (13) |
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13.3.1 Compressive Sensing Detection |
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442 | (3) |
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13.3.2 Statistics of the Error of Compressive Signal Recovery |
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445 | (3) |
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13.3.3 Threshold Estimation for Compressive Detection |
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448 | (2) |
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13.3.4 GPD and Compressive Sensing |
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450 | (1) |
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13.3.5 Computational Complexity of GPD-Based Threshold Estimation |
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451 | (4) |
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13.3.5.1 Performance of GPD-Based Threshold Estimation |
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452 | (3) |
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13.4 Conclusions and Future Work |
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455 | (2) |
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13.4.1 Compressive Noise Radar Imaging and Detection |
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455 | (1) |
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456 | (1) |
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457 | (4) |
Index |
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461 | |