Study on Signal Detection and Recovery Methods with Joint Sparsity. Doctoral Thesis accepted by Tsinghua University, Beijing, China

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 of signals in practice. The fact that multiple sparse signals share the common locations of dominant coefficients is called by joint sparsity. In the context of signal processing, 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 joint sparse signals and their corresponding theoretical performance analysis, and methods for joint sparse signal recovery and their application in the context of radar imaging. Supervisor’s Foreword Preface Acknowledgments Contents Abbreviations 1 Introduction 1.1 Background 1.2 Related Works 1.2.1 Detection Methods for Jointly Sparse Signals 1.2.2 Recovery Methods for Jointly Sparse Signals 1.3 Main Content and Organization References 2 Detection of Jointly Sparse Signals via Locally Most Powerful Tests with Gaussian Noise 2.1 Introduction 2.2 Signal Model for Jointly Sparse Signal Detection 2.3 LMPT Detection Based on Analog Data 2.3.1 Detection Method 2.3.2 Theoretical Analysis of Detection Performance 2.4 LMPT Detection Based on Coarsely Quantized Data 2.4.1 Detection Method 2.4.2 Quantizer Design and the Effect of Quantization on Detection Performance 2.5 Simulation Results 2.5.1 Simulation Results of the LMPT Detector with Analog Data 2.5.2 Simulation Results of the LMPT Detector with Quantized Data 2.6 Conclusion References 3 Detection of Jointly Sparse Signals via Locally Most Powerful Tests with Generalized Gaussian Model 3.1 Introduction 3.2 The LMPT Detector Based on Generalized Gaussian Model and Its Detection Performance 3.2.1 Generalized Gaussian Model 3.2.2 Signal Detection Method 3.2.3 Theoretical Analysis of Detection Performance 3.3 Quantizer Design and Analysis of Asymptotic Relative Efficiency 3.3.1 Quantizer Design 3.3.2 Asymptotic Relative Efficiency 3.4 Simulation Results 3.5 Conclusion References 4 Jointly Sparse Signal Recovery Method Based on Look-Ahead-Atom-Selection 4.1 Introduction 4.2 Background of Recovery of Jointly Sparse Signals 4.3 Signal Recovery Method Based on Look-Ahead-Atom-Selection and Its Performance Analysis 4.3.1 Signal Recovery Method 4.3.2 Performance Analysis 4.4 Experimental Results 4.5 Conclusion References 5 Signal Recovery Methods Based on Two-Level Block Sparsity 5.1 Introduction 5.2 Signal Recovery Method Based on Two-Level Block Sparsity with Analog Measurements 5.2.1 PGM-Based Two-Level Block Sparsity 5.2.2 Two-Level Block Matching Pursuit 5.3 Signal Recovery Method Based on Two-Level Block Sparsity with 1-Bit Measurements 5.3.1 Background of Sparse Signal Recovery Based on 1-Bit Measurements 5.3.2 Enhanced-Binary Iterative Hard Thresholding 5.4 Simulated and Experimental Results 5.4.1 Simulated and Experimental Results Based on Analog Data 5.4.2 Simulated and Experimental Results Based on 1-Bit Data 5.5 Conclusion References 6 Summary and Perspectives 6.1 Summary 6.2 Perspectives References Appendix A Proof of (2.61) Appendix B Proof of Lemma 1 Appendix C Proof of (3.6) Appendix D Proof of Theorem 1 Appendix E Proof of Lemma 2 About the Author