基于联合稀疏的信号检测与恢复方法研究（英文版）

　　本书围绕联合稀疏信号的检测和恢复，主要研究了联合稀疏信号的检测方法及其检测性能界限、联合稀疏信号的恢复方法及其在雷达成像问题中的应用；介绍了基于局部**势检验的联合稀疏信号检测方法，分析了该方法在模拟数据、低比特量化数据、高斯和广义高斯噪声情形下的理论检测性能。同时，介绍了一种基于前瞻基信号选择和双块稀疏性的联合稀疏信号恢复方法，并以多极化雷达成像为应用实例，介绍了联合稀疏信号的恢复方法；通过改善雷达图像中非零像素点的聚集程度和抑制目标区域外的能量泄露，提升了雷达的成像质量。 本书可供从事通信、雷达等信号处理的研究人员参考、学习。

　　王学谦，2020年毕业于清华大学信息与通信工程专业，导师为李刚教授。现在清华大学从事博士后研究，导师为何友院士，研究方向为稀疏信号处理、信息融合、遥感图像处理、雷达成像、目标检测。近5年以第一作者发表SCI期刊文章10篇（其中包括8篇IEEE长文），以第一作者发表EI国际会议文章4篇，已授权专利4项。获北京市优秀毕业生、清华大学水木学者、清华大学优秀博士毕业论文等荣誉，主持国家博士后创新人才支持计划、博士后面上基金项目。

 
 
 
 
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