基于联合稀疏的信号检测与恢复方法研究(英文版)

1 Introduction 1
1.1 Background 1
1.2 Related Works 4
1.2.1 Detection Methods for Jointly Sparse Signals 4
1.2.2 Recovery Methods for Jointly Sparse Signals 5
1.3 Main Content and Organization 9
References 12 2 Detection of Jointly Sparse Signals via Locally Most Powerful Tests with Gaussian Noise 17
2.1 Introduction 17
2.2 Signal Model for Jointly Sparse Signal Detection 18
2.3 LMPT Detection Based on Analog Data 20
2.3.1 Detection Method 20
2.3.2 Theoretical Analysis of Detection Performance 23
2.4 LMPT Detection Based on Coarsely Quantized Data 25
2.4.1 Detection Method 26
2.4.2 Quantizer Design and the Effect of Quantization on Detection Performance 28
2.5 Simulation Results 33
2.5.1 Simulation Results of the LMPT Detector with Analog Data 33
2.5.2 Simulation Results of the LMPT Detector with Quantized Data 35
2.6 Conclusion 40
References 40 3 Detection of Jointly Sparse Signals via Locally Most Powerful Tests with Generalized Gaussian Model 43
3.1 Introduction 43
3.2 The LMPT Detector Based on Generalized Gaussian Model and Its Detection Performance 43
3.2.1 Generalized Gaussian Model 44
3.2.2 Signal Detection Method 46
3.2.3 Theoretical Analysis of Detection Performance 49
3.3 Quantizer Design and Analysis of Asymptotic Relative Efficiency 50
3.3.1 Quantizer Design 50
3.3.2 Asymptotic Relative Ef?ciency 53
3.4 Simulation Results 54
3.5 Conclusion 59
References 59 4 Jointly Sparse Signal Recovery Method Based on Look-Ahead-Atom-Selection 61
4.1 Introduction 61
4.2 Background of Recovery of Jointly Sparse Signals 62
4.3 Signal Recovery Method Based on Look-Ahead-Atom-Selection and Its Performance Analysis 64
4.3.1 Signal Recovery Method 65
4.3.2 Performance Analysis 67
4.4 Experimental Results 69
4.5 Conclusion 75
References 75 5 Signal Recovery Methods Based on Two-Level Block Sparsity 77
5.1 Introduction 77
5.2 Signal Recovery Method Based on Two-Level Block Sparsity with Analog Measurements 79
5.2.1 PGM-Based Two-Level Block Sparsity 79
5.2.2 Two-Level Block Matching Pursuit 83
5.3 Signal Recovery Method Based on Two-Level Block Sparsity with 1-Bit Measurements 86
5.3.1 Background of Sparse Signal Recovery Based on 1-Bit Measurements 87
5.3.2 Enhanced-Binary Iterative Hard Thresholding 89
5.4 Simulated and Experimental Results 94
5.4.1 Simulated and Experimental Results Based on Analog Data 94
5.4.2 Simulated and Experimental Results Based on 1-Bit Data 99
5.5 Conclusion 104
References 105 6 Summary and Perspectives 107
6.1 Summary 107
6.2 Perspectives 109
References 110
Appendix A: Proof of (2.61) 111
Appendix B: Proof of Lemma 1 113
Appendix C: Proof of (3.6) 115
Appendix D: Proof of Theorem 1 117
Appendix E: Proof of Lemma 2 119
About the Author 121