دانلود کتاب Compressed Sensing in Information Processing

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ANHA Series Preface Preface Acknowledgements Contents Contributors 1 Hierarchical Compressed Sensing 1.1 Introduction 1.2 Hierarchically Sparse Vectors 1.3 Hierarchical Thresholding and Recovery Algorithms 1.4 Hierarchically Restricted Isometric Measurements 1.4.1 Gaussian Operators 1.4.2 Coherence Measures 1.4.3 Hierarchical Measurement Operators 1.5 Sparse De-mixing of Low-Rank Matrices 1.6 Selected Applications 1.6.1 Channel Estimation in Mobile Communication 1.6.2 Secure Massive Access 1.6.3 Blind Quantum State Tomography 1.7 Conclusion and Outlook References 2 Proof Methods for Robust Low-Rank Matrix Recovery 2.1 Introduction 2.1.1 Sample Applications 2.1.1.1 Matrix Completion 2.1.1.2 Blind Deconvolution 2.1.1.3 Phase Retrieval 2.1.2 This Work 2.2 Recovery Guarantees via a Descent Cone Analysis 2.2.1 Descent Cone Analysis 2.2.2 Application 1: Generic Low-Rank Matrix Recovery 2.2.3 Application 2: Phase Retrieval 2.2.4 Limitations 2.3 Recovery Guarantees via the Golfing Scheme 2.3.1 Recovery Guarantees via Dual Certificates 2.3.2 Golfing with Precision 2.3.3 Application 3: Matrix Completion 2.3.4 Application 4: Simultaneous Demixing and Blind Deconvolution 2.3.5 Phase Retrieval with Incoherence 2.4 More Refined Descent Cone Analysis 2.4.1 Application 5: Blind Deconvolution 2.4.2 Application 6: Phase Retrieval with Incoherence 2.5 Conclusion Appendix: Descent Cone Elements Are Effectively Low Rank References 3 New Challenges in Covariance Estimation: Multiple Structures and Coarse Quantization 3.1 Introduction 3.1.1 Outline and Notation 3.2 Motivation: Massive MIMO 3.3 Estimation of Structured Covariance Matrices and Robustness Against Outliers 3.3.1 Sparse Covariance Matrices 3.3.2 Low-Rank Covariance Matrices 3.3.3 Toeplitz Covariance Matrices and Combined Structures 3.4 Estimation from Quantized Samples 3.4.1 Sign Quantization 3.4.2 Dithered Quantization 3.5 The Underlying Structures of Massive MIMO Covariance Estimation 3.6 Conclusion Appendix: Proof of Theorem 3.6 References 4 Sparse Deterministic and Stochastic Channels: Identification of Spreading Functions and Covariances 4.1 Motivation and Introduction 4.2 Channel Identification and Estimation 4.2.1 Time–Frequency Analysis in Finite Dimensions 4.2.2 Deterministic Channels 4.2.3 Stochastic Channels 4.3 Results in Deterministic Setting 4.3.1 Classical Results on Channel Identification 4.3.1.1 Identification of SISO Channels 4.3.1.2 Identification of MIMO Channels 4.3.2 Linear Constraints 4.3.3 Message Transmission Using Unidentified Channels 4.3.3.1 Problem Formulation 4.3.3.2 Message Transmission with Known Support 4.3.3.3 Message Transmission with Unknown Support 4.4 Results in Stochastic Setting 4.4.1 Permissible and Defective Support Patterns 4.4.2 Linear Constraints in Stochastic Setting 4.4.2.1 WSSUS Pattern with Additional Off-diagonal Contributions 4.4.2.2 Tensor Product Pattern with Additional Contributions 4.4.3 Numerical Simulations Appendix Proof of Lemma 4.3 Proof of Proposition 4.6 Proof of Proposition 4.7 Proof of Proposition 4.8 Proof of Proposition 4.10 Proof of Proposition 4.11 References 5 Analysis of Sparse Recovery Algorithms via the Replica Method 5.1 Introduction 5.2 A Multi-terminal Setting for Compressive Sensing 5.2.1 Characterization of the Recovery Performance 5.2.2 Stochastic Model of System Components 5.2.3 Stochastic Model for Jointly Sparse Signals 5.2.4 Special Cases 5.2.4.1 Classical Compressive Sensing 5.2.4.2 Multiple Measurement Vectors 5.2.4.3 Distributed Compressive Sensing 5.3 Sparse Recovery via the Regularized Least-Squares Method 5.3.1 Some Well-Known Forms 5.3.1.1 p-Norm Minimization 5.3.1.2 p,q-Norm Minimization 5.3.2 Bayesian Interpretation 5.4 Asymptotic Characterization 5.4.1 Stieltjes and R-Transforms 5.5 Building a Bridge to Statistical Mechanics 5.5.1 Introduction to Statistical Mechanics 5.5.1.1 Second Law of Thermodynamics 5.5.1.2 Spin Glasses 5.5.1.3 Thermodynamic Limit 5.5.1.4 Averaging Trick 5.5.2 Corresponding Spin Glass 5.5.2.1 Asymptotic Distortion as a Macroscopic Parameter 5.5.3 The Replica Method 5.6 The Replica Analysis 5.6.1 General Form of the Solution 5.6.2 Constructing Parameterized Qj 5.6.2.1 Replica Symmetric Solution 5.6.2.2 Replica Symmetry Breaking 5.7 Applications and Numerical Results 5.7.1 Performance Analysis of Sparse Recovery 5.7.2 Tuning RLS-Based Algorithms 5.8 Summary and Final Discussions 5.8.1 Decoupling Principle 5.8.2 Nonuniform Sparsity Patterns 5.8.3 Extensions to Bayesian Estimation 5.9 Bibliographical Notes References 6 Unbiasing in Iterative Reconstruction Algorithms for Discrete Compressed Sensing 6.1 Introduction 6.1.1 Compressed Sensing Problem and Reconstruction Algorithms 6.1.2 Discrete Setting 6.1.3 Outline of the Chapter 6.2 Problem Statement and Iterative Algorithms 6.2.1 Factorization and Message-Passing Approaches 6.2.1.1 Message-Passing Approaches 6.2.1.2 Partitioning of the Problem 6.2.2 Exponential Families 6.3 Expectation-Consistent Approximate Inference 6.3.1 Derivation and Optimization Procedure 6.3.2 Algorithms 6.3.2.1 Optimization: ECopts, ECoptc and ECseqs, ECseqc 6.3.2.2 Vector Approximate Message Passing: VAMP 6.3.2.3 Discussion 6.3.3 Alternative Partitioning of the Problem 6.4 Unbiasing of MMSE Estimators 6.4.1 Joint Linear Estimators 6.4.1.1 Average Unbiasing 6.4.1.2 Individual Unbiasing 6.4.2 Scalar Non-linear Estimators 6.4.2.1 Signal-Oriented Unbiasing 6.4.2.2 Noise-Oriented Unbiasing 6.4.3 Iterative Schemes with Individual and Average Variances 6.5 Numerical Results and Discussion 6.5.1 Average Variance 6.5.2 Individual Variances References 7 Recovery Under Side Constraints 7.1 Introduction 7.2 Sparse Recovery in Sensor Arrays 7.2.1 Compressive Data Model for Sensor Arrays 7.2.2 Sparse Recovery Formulations for Sensor Arrays 7.3 Recovery Guarantees Under Side Constraints 7.3.1 Integrality Constraints 7.3.2 General Framework for Arbitrary Side Constraints 7.4 Recovery Algorithms Under Different Side Constraints for the Linear Measurement Model 7.4.1 Constant-Modulus Constraints 7.4.2 Row- and Rank-Sparsity 7.4.3 Block-Sparse Tensors 7.4.4 Non-circularity 7.5 Mixing Matrix Design 7.5.1 Sensing Matrix Design: P = M Case 7.5.2 Sensing Matrix Design: The General Case 7.5.3 Numerical Results 7.6 Recovery Algorithms for the Nonlinear Measurement Model 7.6.1 Sparse Phase Retrieval 7.6.2 Phase Retrieval with Dictionary Learning 7.7 Conclusions References 8 Compressive Sensing and Neural Networks from a Statistical Learning Perspective 8.1 Introduction 8.1.1 Notation 8.2 Deep Learning and Inverse Problems 8.2.1 Learned Iterative Soft Thresholding 8.2.2 Variants of LISTA 8.3 Generalization of Deep Neural Networks 8.3.1 Rademacher Complexity Analysis 8.3.2 Generalization Bounds for Deep Neural Networks 8.4 Generalization of Deep Thresholding Networks 8.4.1 Boundedness: Assumptions and Results 8.4.2 Dudley's Inequality 8.4.3 Bounding the Rademacher Complexity 8.4.4 A Perturbation Result 8.4.5 Covering number estimates 8.4.6 Main result 8.5 Thresholding Networks for Sparse Recovery 8.6 Conclusion and Outlook References 9 Angular Scattering Function Estimation Using Deep Neural Networks 9.1 Introduction 9.1.1 Related Work 9.1.2 Outline and Notation 9.2 System Model 9.3 The Parametric Form of ASF 9.3.1 The Continuous ASF Component 9.3.2 The Discrete ASF Component 9.4 Pre-processing: Discrete AoA Estimation via MUSIC 9.5 A Deep Learning Approach to ASF Estimation 9.5.1 Training Phase 9.5.2 Network Architecture 9.5.3 Test Phase 9.6 Simulation Results 9.6.1 Metrics for Comparison 9.6.2 Performance with Different SNRs 9.6.3 Performance with Different Sample Numbers 9.7 Conclusion References 10 Fast Radio Propagation Prediction with Deep Learning 10.1 Introduction 10.1.1 Applications of Radio Maps 10.1.2 Radio Map Prediction 10.1.3 Radio Map Prediction Using Deep Learning 10.2 Introduction to Radio Map Prediction with RadioUNet 10.2.1 RadioUNet Methods 10.2.2 The Training Data 10.2.3 Generalizing What Was Learned to Real-Life Scenarios 10.2.4 Applications 10.3 Background and Preliminaries 10.3.1 Wireless Communication 10.3.2 Deep Learning 10.3.2.1 An Interpretation of Deep Learning 10.3.2.2 Convolutional Neural Networks 10.3.2.3 UNets 10.3.2.4 Supervised Learning of UNets via Stochastic Gradient Descent 10.3.2.5 Curriculum Learning 10.3.2.6 Out-of-Domain Generalization 10.4 The RadioMapSeer Dataset 10.4.1 General Setting 10.4.1.1 Maps and Transmitters 10.4.1.2 Coarsely Simulated Radio Maps 10.4.1.3 Higher-Accuracy Simulations 10.4.1.4 Pathloss Scale 10.4.2 System Parameters 10.4.3 Gray-Level Conversion 10.5 Estimating Radio Maps via RadioUNets 10.5.1 Motivation for RadioUNet 10.5.2 Different Settings in Radio Map Estimation 10.5.2.1 Network Input Scenarios 10.5.2.2 Learning Scenarios 10.5.3 RadioUNet Architectures 10.5.3.1 Retrospective Improvement 10.5.3.2 Adaptation to Real Measurements 10.5.3.3 Thresholder 10.5.4 Training 10.5.5 RadioUNet Performance 10.6 Comparison of RadioUNet to State of the Art 10.6.1 Comparison to Model-Based Simulation 10.6.2 Comparison to Data-Driven Interpolation 10.6.3 Comparison to Model-Based Data Fitting 10.6.4 Comparison to Deep Learning Data Fitting 10.7 Applications 10.7.1 Coverage Classification 10.7.2 Pathloss-Based Fingerprint Localization 10.8 Conclusion References 11 Active Channel Sparsification: Realizing Frequency-Division Duplexing Massive MIMO with Minimal Overhead 11.1 Introduction 11.2 System Model 11.2.1 Related Work 11.2.2 Contribution 11.3 Channel Model 11.4 Active Channel Sparsification and DL Channel Training 11.4.1 Necessity and Implication of Stable Channel Estimation 11.4.2 Sparsifying Precoder Design 11.4.3 Channel Estimation and Multiuser Precoding 11.5 Simulation Results 11.5.1 Channel Estimation Error and Sum Rate vs. Pilot Dimension 11.5.2 The Effect of Channel Sparsity 11.6 Beam-Space Design for Arbitrary Array Geometries 11.6.1 Jointly Diagonalizable Covariances 11.6.2 ML via Projected Gradient Descent 11.6.3 Extension of ACS to Arbitrary Array Geometries References 12 Atmospheric Radar Imaging Improvements Using Compressed Sensing and MIMO 12.1 Introduction 12.2 System Model and Inversion Methods for Atmospheric Radar Imaging 12.2.1 System Model for SIMO Atmospheric Radar Imaging 12.2.2 System Model for MIMO Atmospheric Radar Imaging 12.2.3 SIMO vs MIMO Arrays 12.2.4 Inversion Methods 12.2.4.1 The Capon Method 12.2.4.2 Maximum Entropy Method 12.2.4.3 Compressed Sensing 12.2.5 MIMO Implementations 12.2.5.1 Time Diversity 12.2.5.2 Waveform Diversity 12.2.5.3 Suboptimal Diversity 12.3 Applications of MIMO in Atmospheric Radar Imaging 12.3.1 MIMO in Atmospheric Radar Imaging for Ionospheric Studies 12.3.2 Polar Mesospheric Summer Echoes Imaging 12.3.3 MIMO in Specular Meteor Radars to Measure Mesospheric Winds 12.4 Summary and Future Work Table of Mathematical Symbols References 13 Over-the-Air Computation for Distributed Machine Learning and Consensus in Large Wireless Networks 13.1 Introduction 13.2 Over-the-Air Computation 13.2.1 Digital Over-the-Air Computation 13.2.2 Analog Over-the-Air Computation 13.2.3 Analog Over-the-Air Computation as a Compressed Sensing Problem 13.3 Applications of Over-the-Air Computation 13.3.1 Distributed Machine Learning 13.3.2 Consensus Over Wireless Channels 13.3.3 Compressed Sensing 13.4 Distributed Function Approximation in Wireless Channels 13.4.1 Class of Functions 13.4.2 System and Channel Model 13.4.3 The Case of Independent Fading and Noise 13.4.4 The Case of Correlated Fading and Noise 13.5 DFA Applications to VFL 13.6 Security in OTA Computation 13.6.1 Information-Theoretic Preliminaries 13.6.2 Result and Discussion 13.7 Open Research Questions References 14 Information Theory and Recovery Algorithms for Data Fusion in Earth Observation 14.1 General Framework 14.2 Identification of Neural Networks: From One Neuron to Deep Neural Networks 14.2.1 From One Neuron to Deep Networks 14.2.2 Data Interpolation and Identification of Neural Networks 14.2.3 Shallow Feed-Forward Neural Networks 14.2.3.1 The Approximation to W: Active Sampling 14.2.3.2 Whitening 14.2.3.3 The Recovery Strategy of the Weights wi 14.2.4 Deeper Networks 14.3 Quantized Compressed Sensing with Message Passing Reconstruction 14.3.1 Bayesian Compressed Sensing via Approximate Message Passing 14.3.2 Two-Terminal Bayesian QCS 14.4 Signal Processing in Earth Observation 14.4.1 Multi-Sensor and Multi-Resolution Data Fusion 14.4.2 Hyperspectral Unmixing Accounting for Spectral Variability References 15 Sparse Recovery of Sound Fields Using Measurements from Moving Microphones 15.1 Problem Formulation and Signal Model 15.1.1 General Problem 15.1.2 Sparse Signal Structures 15.2 Multidimensional Sampling and Reconstruction 15.2.1 Temporal Sampling Model 15.2.2 Spatial Sampling Model 15.2.3 Spatio-Temporal Measurement Model 15.2.3.1 Finite-Length Observations in Space 15.2.3.2 Linear Equations for Parameter Recovery in Terms of Uniform Grids 15.3 Sparse Sound-Field Recovery in Frequency Domain 15.3.1 Basic Ideas for the Simplified Stationary Case 15.3.2 From Static to Dynamic Sensing 15.3.3 Sparse Recovery Along the Spectral Hypercone 15.3.4 Perfect Excitation Sequences 15.3.5 Algorithm for Sparse Recovery from Dynamic Measurements 15.3.5.1 General Case 15.3.5.2 Perfect-Excitation Case 15.4 Coherence Analysis 15.4.1 Influence of the Trajectory on the Sensing Matrix 15.4.2 Coherence of Measurements 15.4.3 Spectrally Flat Spatio-Temporal Excitation 15.5 Trajectory Optimization 15.5.1 Techniques for Measurement Matrix Optimization 15.5.2 Fast Update Scheme for Trajectory Adjustments 15.6 Summary References 16 Compressed Sensing in the Spherical Near-Field to Far-Field Transformation 16.1 Spherical Near-Field Antenna Measurements 16.1.1 Notation 16.2 Compressed Sensing 16.3 Definition and Backgrounds 16.3.1 Wigner D-Functions and Spherical Harmonics 16.3.2 Sparse Expansions of Band-Limited Functions 16.3.3 Construction of the Sensing Matrix 16.3.3.1 RIP Condition for Sensing Matrices 16.3.3.2 Construction of Low-Coherence Sensing Matrices 16.3.4 Numerical Evaluation 16.3.4.1 Coherence Evaluation 16.3.4.2 Phase Transition Diagram: Random vs. Deterministic 16.3.5 Implementation in Spherical Near-Field Antenna Measurements 16.3.5.1 Modifying the Scheme for Time Efficiency 16.3.5.2 Extension to Arbitrary Surfaces 16.3.5.3 Implementation Considerations: Basis Mismatch 16.4 Phaseless Spherical Near-Field Antenna Measurements 16.4.1 Phaseless Measurements 16.4.1.1 Ambiguities in Phaseless Spherical Harmonics Expansion 16.4.2 Numerical Evaluation 16.4.2.1 Phase Transition Diagram 16.4.2.2 Implementation in Spherical Near-Field Antenna Measurements 16.5 Summary References Applied and Numerical Harmonic Analysis Applied and Numerical Harmonic Analysis (104 volumes)