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
內容試閱：
The task of signal detection is deciding whether signals of interest exist by using their observed data. Furthermore， signals are reconstructed or their key parameters are estimated from the observations in the task of signal recovery. Sparsity is a natural characteristic of most signals in practice. The fact that multiple sparse signals share the common locations of dominant coef.cients is called joint sparsity. In the context of signal processing， the joint sparsity model results in higher performance of signal detection and recovery. This book focuses on the task of detecting and reconstructing signals with joint sparsity. The main contents include key methods for detection of jointly sparse signals and their corresponding theoretical performance analysis and methods for jointly sparse signal recovery and their application in the context of radar imaging. The main contribution of this book is as follows:
(1)
For the problem of detection of jointly sparse signals， a method is proposed based on the strategy of the locally most powerful test. The theoretical detec-tion performance of this method is provided in the cases of analog observa-tions， coarsely quantized observations， Gaussian noise， and non-Gaussian noise， respectively. For the problem of signal detection with quantized observations， the thresholds of optimal quantizer are solved， and the detection performance loss caused by quantization is quantitatively evaluated with the optimal quan-tizer. The strategy of compensating for the detection performance loss caused by quantization is also provided. Compared with existing detection methods， the proposed method signi.cantly reduces the computational and communication burden without noticeable detection performance loss.
(2)
For the problem of recovery of jointly sparse signals， a method is proposed based on the selection of atoms with the look-ahead strategy. Atoms correspond to the locations of nonzero values in sparse signals. This method evaluates the effect of the selection of atoms on future recovery error in the iterative process. Theoretical analysis indicates that the proposed method improves the stability in the selection of atoms. The application of this method in the .eld of multiple-channel radar imaging is considered. Experiments based on real radar
data demonstrate that the proposed method improves the accuracy of signal recovery with joint sparsity and reduces the number of artifacts in radar images.
(3) For the problem of recovery of jointly sparse signals， a method is proposed based on the two-level block sparsity， which combines not only the joint spar-sity of multiple signals but also the clustering structure in each sparse signal. Experimental results based on real radar data show that， compared with existing methods， the dominant pixels in radar images generated by the proposed method are more concentrated in the target area， and there is less energy leak in the non-target area， i.e.， better imaging quality is provided by the proposed method. Furthermore， this method is extended to the 1-bit quantization scenario to reduce the hardware consumption of radar imaging systems. Experiments based on real radar data demonstrate that the proposed method based on the two-level block sparsity signi.cantly improves the quality of 1-bit radar imaging.
This book is organized as follows. In Chap. 1， the background and related works of joint sparsity are brie.y reviewed. In Chaps. 2 and 3， the joint sparsity-driven signal detection methods in the context of Gaussian and non-Gaussian noise environments are presented to accelerate existing methods， respectively. In Chaps. 4 and 5， the joint sparsity-driven signal recovery methods based on look-ahead-atom-selection and two-level block sparsity are studied to enhance the performance of radar imaging. Chapter 6 summarizes the book and discusses future perspectives.
I do hope that this book could be a good reference to undergraduate/graduate students and researchers in the areas of signal processing and radar imaging and to provide theoretical and technical support in their research and engineering works.
Beijing， China Xueqian Wang
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