Message Passing Algorithms for Compressed Sensing

Abstract

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a known basis. Currently, the best known sparsity-undersampling tradeoff is achieved when reconstructing by convex optimization -- which is expensive in important large-scale applications. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for large-scale problems. Unfortunately known fast algorithms offer substantially worse sparsity-undersampling tradeoffs than convex optimization. We introduce a simple costless modification to iterative thresholding making the sparsity-undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures. The new iterative-thresholding algorithms are inspired by belief propagation in graphical models. Our empirical measurements of the sparsity-undersampling tradeoff for the new algorithms agree with theoretical calculations. We show that a state evolution formalism correctly derives the true sparsity-undersampling tradeoff. There is a surprising agreement between earlier calculations based on random convex polytopes and this new, apparently very different theoretical formalism.

6 pages paper + 9 pages supplementary information, 13 eps figure. Submitted to Proc. Natl. Acad. Sci. USA

References in corpus (4)

• Observed Universality of Phase Transitions in High-Dimensional Geometry, with Implications for Modern Data Analysis and Signal Processing
• Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing
• Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing
• Efficient and Robust Compressed Sensing using High-Quality Expander Graphs

Cited by in corpus (565)

• A survey of sparse representation: algorithms and applications
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• The dynamics of message passing on dense graphs, with applications to compressed sensing
• Massive Connectivity with Massive MIMO-Part I: Device Activity Detection and Channel Estimation
• Machine Learning at the Wireless Edge: Distributed Stochastic Gradient Descent Over-the-Air
• Sparse Signal Processing for Grant-Free Massive Connectivity: A Future Paradigm for Random Access Protocols in the Internet of Things
• Expectation-Maximization Gaussian-Mixture Approximate Message Passing
• Rank Minimization for Snapshot Compressive Imaging
• AMP-Inspired Deep Networks for Sparse Linear Inverse Problems
• Model-Driven Deep Learning for MIMO Detection
• Statistical physics of inference: Thresholds and algorithms
• Sparse Activity Detection for Massive Connectivity
• Bayes-Optimal Joint Channel-and-Data Estimation for Massive MIMO with Low-Precision ADCs
• DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing
• A Deep Learning Approach to Structured Signal Recovery
• Matrix-Calibration-Based Cascaded Channel Estimation for Reconfigurable Intelligent Surface Assisted Multiuser MIMO
• AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing
• Bilinear Generalized Approximate Message Passing
• Compressive Phase Retrieval via Generalized Approximate Message Passing
• Plug and play methods for magnetic resonance imaging (long version)
• A modern maximum-likelihood theory for high-dimensional logistic regression
• Trainable ISTA for Sparse Signal Recovery
• Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior
• Universality in polytope phase transitions and message passing algorithms
• An Online Plug-and-Play Algorithm for Regularized Image Reconstruction
• Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models
• Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
• Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• A weighted L1-minimization approach for sparse polynomial chaos expansions
• Statistical physics-based reconstruction in compressed sensing
• Turbo Compressed Sensing with Partial DFT Sensing Matrix
• Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem
• Massive Connectivity with Massive MIMO-Part II: Achievable Rate Characterization
• Robustly Stable Signal Recovery in Compressed Sensing with Structured Matrix Perturbation
• SPARCs for Unsourced Random Access
• Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation
• EfficientFi: Towards Large-Scale Lightweight WiFi Sensing via CSI Compression
• Low-complexity Multiclass Encryption by Compressed Sensing
• Regime Change: Bit-Depth versus Measurement-Rate in Compressive Sensing
• Entropy and mutual information in models of deep neural networks
• Message-Passing Estimation from Quantized Samples
• Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
• Measure What Should be Measured: Progress and Challenges in Compressive Sensing
• Sparsity Learning Based Multiuser Detection in Grant-Free Massive-Device Multiple Access
• Mixed-ADC Massive MIMO Detectors: Performance Analysis and Design Optimization
• Content-aware Scalable Deep Compressed Sensing
• An Adaptive and Robust Deep Learning Framework for THz Ultra-Massive MIMO Channel Estimation
• Phase transitions and sample complexity in Bayes-optimal matrix factorization
• Phase Transitions in Semidefinite Relaxations
• A Message-Passing Receiver for BICM-OFDM over Unknown Clustered-Sparse Channels
• Mean-field message-passing equations in the Hopfield model and its generalizations
• Fast L1-Minimization Algorithms For Robust Face Recognition
• Image Compressed Sensing Using Non-local Neural Network
• MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel
• Multi-Cell Sparse Activity Detection for Massive Random Access: Massive MIMO versus Cooperative MIMO
• Compressive Hyperspectral Imaging via Approximate Message Passing
• Compressive Imaging via Approximate Message Passing with Image Denoising
• The LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
• Recursive Recovery of Sparse Signal Sequences from Compressive Measurements: A Review
• Constrained Low-rank Matrix Estimation: Phase Transitions, Approximate Message Passing and Applications
• Clustering-Based Activity Detection Algorithms for Grant-Free Random Access in Cell-Free Massive MIMO
• On Convergence of Approximate Message Passing
• Learning optimal nonlinearities for iterative thresholding algorithms
• Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigms
• Unitary Approximate Message Passing for Sparse Bayesian Learning
• Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators : rigorous results
• Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models
• On asymptotic structure in compressed sensing
• A statistical model for tensor PCA
• A Unified Bayesian Inference Framework for Generalized Linear Models
• Statistical mechanics of complex neural systems and high dimensional data
• A Factor Graph Approach to Joint OFDM Channel Estimation and Decoding in Impulsive Noise Environments
• Bayesian User Localization and Tracking for Reconfigurable Intelligent Surface Aided MIMO Systems
• The Mutual Information in Random Linear Estimation
• Near optimal compressed sensing without priors: Parametric SURE Approximate Message Passing
• Joint k-step analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares
• Statistical estimation and testing via the sorted L1 norm
• Belief propagation for joint sparse recovery
• Message-passing algorithms for synchronization problems over compact groups
• Fundamental limits of many-user MAC with finite payloads and fading
• Hybrid Approximate Message Passing
• Breaking the coherence barrier: A new theory for compressed sensing
• A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices
• Parametric Bilinear Generalized Approximate Message Passing
• On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices
• A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions
• The Phase Transition of Matrix Recovery from Gaussian Measurements Matches the Minimax MSE of Matrix Denoising
• Approximate Message Passing with Unitary Transformation
• The distribution of the Lasso: Uniform control over sparse balls and adaptive parameter tuning
• Learning curves of generic features maps for realistic datasets with a teacher-student model
• Cross validation in LASSO and its acceleration
• Symbol Error Rate Performance of Box-relaxation Decoders in Massive MIMO
• Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes
• Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
• Provable Convergence of Plug-and-Play Priors with MMSE denoisers
• Analysis of Regularized LS Reconstruction and Random Matrix Ensembles in Compressed Sensing
• Unsupervised Learning with Stein's Unbiased Risk Estimator
• Sparse Activity Detection in Multi-Cell Massive MIMO Exploiting Channel Large-Scale Fading
• Convolutional Proximal Neural Networks and Plug-and-Play Algorithms
• Reconstruction of Signals Drawn from a Gaussian Mixture from Noisy Compressive Measurements
• Orthogonal Matching Pursuit with Replacement
• Networking - A Statistical Physics Perspective
• Location Identification of Power Line Outages Using PMU Measurements with Bad Data
• Computational Barriers to Estimation from Low-Degree Polynomials
• Sparse Modeling in Quantum Many-Body Problems
• Generalized Approximate Message Passing for Estimation with Random Linear Mixing
• Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization
• Finite Sample Analysis of Approximate Message Passing Algorithms
• Plug-in Estimation in High-Dimensional Linear Inverse Problems: A Rigorous Analysis
• Typology of phase transitions in Bayesian inference problems
• The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
• Replica Analysis and Approximate Message Passing Decoder for Superposition Codes
• An Empirical-Bayes Approach to Recovering Linearly Constrained Non-Negative Sparse Signals
• Compressive Spectral Image Reconstruction using Deep Prior and Low-Rank Tensor Representation
• Sparse Regression Codes
• Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
• Fundamental limits of low-rank matrix estimation: the non-symmetric case
• Sparse Estimation with the Swept Approximated Message-Passing Algorithm
• High-temperature Expansions and Message Passing Algorithms
• ReconNet: Non-Iterative Reconstruction of Images from Compressively Sensed Random Measurements
• Phase Diagram and Approximate Message Passing for Blind Calibration and Dictionary Learning
• Random Access in C-RAN for User Activity Detection with Limited-Capacity Fronthaul
• Asymptotic Mutual Information for the Two-Groups Stochastic Block Model
• Mean-field inference methods for neural networks
• Wave-Like Solutions of General One-Dimensional Spatially Coupled Systems
• Super-Resolution Blind Channel-and-Signal Estimation for Massive MIMO with One-Dimensional Antenna Array
• Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing
• Region graph partition function expansion and approximate free energy landscapes: Theory and some numerical results
• Mean field analysis of reverse annealing for code-division multiple-access multiuser detection
• Optimized projections for compressed sensing via rank-constrained nearest correlation matrix
• Bilinear Recovery using Adaptive Vector-AMP
• Understanding overfitting peaks in generalization error: Analytical risk curves for $l_2$ and $l_1$ penalized interpolation
• Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference
• Multi-Layer Generalized Linear Estimation
• A New Insight into GAMP and AMP
• Convolutional Approximate Message-Passing
• Finding Hidden Cliques of Size \sqrt{N/e} in Nearly Linear Time
• Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)
• Performance Analysis and Approximate Message Passing Detection of Orthogonal Time Sequency Multiplexing Modulation
• Generalized Turbo Signal Recovery for Nonlinear Measurements and Orthogonal Sensing Matrices
• Approximate Message Passing Algorithm with Universal Denoising and Gaussian Mixture Learning
• On Phase Transition of Compressed Sensing in the Complex Domain
• Statistical mechanics of unsupervised feature learning in a restricted Boltzmann machine with binary synapses
• Parameterless Optimal Approximate Message Passing
• Forest Sparsity for Multi-channel Compressive Sensing
• Multi-Layer Bilinear Generalized Approximate Message Passing
• Living on the edge: Phase transitions in convex programs with random data
• Approximate Message Passing with Restricted Boltzmann Machine Priors
• High-dimensional macroeconomic forecasting using message passing algorithms
• The committee machine: Computational to statistical gaps in learning a two-layers neural network
• The Asymptotic Distribution of the MLE in High-dimensional Logistic Models: Arbitrary Covariance
• Democratic Representations
• Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks
• MIMO-OFDM-Based Massive Connectivity With Frequency Selectivity Compensation
• Structured LISTA for Multidimensional Harmonic Retrieval
• Glassy nature of the hard phase in inference problems
• On the Performance of Mismatched Data Detection in Large MIMO Systems
• Statistical Tools and Methodologies for Ultrareliable Low-Latency Communications -- A Tutorial
• High Dimensional Robust M-Estimation: Asymptotic Variance via Approximate Message Passing
• Modulated Sparse Superposition Codes for the Complex AWGN Channel
• An Approximate Message Passing Framework for Side Information
• Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing
• Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction
• Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective
• ATASI-Net: An Efficient Sparse Reconstruction Network for Tomographic SAR Imaging with Adaptive Threshold
• Variance State Propagation for Structured Sparse Bayesian Learning
• The Effect of Spatial Coupling on Compressive Sensing
• Statistical Mechanics of High-Dimensional Inference
• Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices
• Binary Linear Classification and Feature Selection via Generalized Approximate Message Passing
• Adaptive Block Compressive Sensing: towards a real-time and low-complexity implementation
• A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-${\ell }_1$-Norm Interpolated Classifiers
• The Error Probability of Sparse Superposition Codes with Approximate Message Passing Decoding
• Performance Limits for Noisy Multi-Measurement Vector Problems
• Phase retrieval in high dimensions: Statistical and computational phase transitions
• Statistical Mechanics of Dictionary Learning
• Compressive MUSIC: A Missing Link Between Compressive Sensing and Array Signal Processing
• Deep Learning for Scene Classification: A Survey
• Coded Demixing for Unsourced Random Access
• Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines
• Approximate Survey Propagation for Statistical Inference
• Asymptotic Analysis of LASSOs Solution Path with Implications for Approximate Message Passing
• Activity Detection in Distributed MIMO: Distributed AMP via Likelihood Ratio Fusion
• Sparse approximation based on a random overcomplete basis
• Bayesian signal reconstruction for 1-bit compressed sensing
• Fast Compressive Sensing Recovery Using Generative Models with Structured Latent Variables
• Signal Estimation with Additive Error Metrics in Compressed Sensing
• Sensing Matrix Design and Sparse Recovery on the Sphere and the Rotation Group
• Scaling Limit: Exact and Tractable Analysis of Online Learning Algorithms with Applications to Regularized Regression and PCA
• A scalable estimate of the extra-sample prediction error via approximate leave-one-out
• Scalable Inference for Neuronal Connectivity from Calcium Imaging
• Tensor Programs III: Neural Matrix Laws
• Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
• Sharp MSE Bounds for Proximal Denoising
• Deep Learning for Massive MIMO CSI Feedback
• Optimal Data Detection in Large MIMO
• Sub-linear Time Support Recovery for Compressed Sensing using Sparse-Graph Codes
• Don't Just Blame Over-parametrization for Over-confidence: Theoretical Analysis of Calibration in Binary Classification
• Learning curves for the multi-class teacher-student perceptron
• Learning Fast Sparsifying Transforms
• Heterogeneous Networked Data Recovery from Compressive Measurements Using a Copula Prior
• Algorithmic Thresholds in Mean Field Spin Glasses
• Fundamental problems in statistical physics XIV: Lecture on Machine Learning
• Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties
• Precise Error Analysis of Regularized M-estimators in High-dimensions
• Massive Uncoordinated Multiple Access for Beyond 5G
• Matrix factorization with neural networks
• Unifying Message Passing Algorithms Under the Framework of Constrained Bethe Free Energy Minimization
• Exact asymptotics for phase retrieval and compressed sensing with random generative priors
• All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation
• Sparse Multinomial Logistic Regression via Approximate Message Passing
• Compressed Sensing under Matrix Uncertainty: Optimum Thresholds and Robust Approximate Message Passing
• Compressed sensing in scanning tunneling microscopy/spectroscopy for observation of quasi-particle interference
• Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing
• Joint Sparsity Pattern Learning Based Channel Estimation for Massive MIMO-OTFS Systems
• Statistical and Algorithmic Insights for Semi-supervised Learning with Self-training
• Decoding from Pooled Data: Phase Transitions of Message Passing
• Does ${\ell }_p$-minimization outperform ${\ell }_1$-minimization?
• Compressed Sensing over ${\ell }_p$-balls: Minimax Mean Square Error
• Denoising based Vector Approximate Message Passing
• Homotopy Analysis for Tensor PCA
• Array SAR 3D Sparse Imaging Based on Regularization by Denoising Under Few Observed Data
• Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning
• Interference-Cancellation-Based Channel Knowledge Map Construction and Its Applications to Channel Estimation
• Riemannian Low-Rank Model Compression for Federated Learning with Over-the-Air Aggregation
• Concise Derivation of Complex Bayesian Approximate Message Passing via Expectation Propagation
• Rigorous Dynamics of Expectation-Propagation-Based Signal Recovery from Unitarily Invariant Measurements
• Statistical mechanical analysis of sparse linear regression as a variable selection problem
• A statistical mechanics approach to de-biasing and uncertainty estimation in LASSO for random measurements
• Spectral Planting and the Hardness of Refuting Cuts, Colorability, and Communities in Random Graphs
• Rate-Distortion Optimal Transform Coefficient Selection for Unoccupied Regions in Video-Based Point Cloud Compression
• Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)
• Optimal Phase Transitions in Compressed Sensing
• Signal Recovery in Unions of Subspaces with Applications to Compressive Imaging
• Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing
• Deep learning via message passing algorithms based on belief propagation
• SignalNet: A Low Resolution Sinusoid Decomposition and Estimation Network
• On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization
• Analysis of Compressed Sensing with Spatially-Coupled Orthogonal Matrices
• PCA Initialization for Approximate Message Passing in Rotationally Invariant Models
• Unsourced Multiuser Sparse Regression Codes achieve the Symmetric MAC Capacity
• Statistical mechanics of low-rank tensor decomposition
• Which bridge estimator is optimal for variable selection?
• Approximate Leave-One-Out for Fast Parameter Tuning in High Dimensions
• Massive MIMO-OFDM Channel Acquisition with Time-Frequency Phase-Shifted Pilots
• Near-optimal matrix recovery from random linear measurements
• Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes
• 0-1 phase transitions in sparse spiked matrix estimation
• Compressed Sensing of Approximately-Sparse Signals: Phase Transitions and Optimal Reconstruction
• Phase transition in random tensors with multiple independent spikes
• Sparsity Enhanced Decision Feedback Equalization
• Sparse Vector Distributions and Recovery from Compressed Sensing
• Uformer-ICS: A U-Shaped Transformer for Image Compressive Sensing Service
• Message Passing Least Squares Framework and its Application to Rotation Synchronization
• Denoising-based Turbo Message Passing for Compressed Video Background Subtraction
• Gradient Projection Newton Pursuit for Sparsity Constrained Optimization
• Compressed sensing reconstruction using Expectation Propagation
• Inference in Deep Networks in High Dimensions
• On the Universality of Noiseless Linear Estimation with Respect to the Measurement Matrix
• Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising
• Performance Limits with Additive Error Metrics in Noisy Multi-Measurement Vector Problem
• Non-adaptive pooling strategies for detection of rare faulty items
• Non-negative Principal Component Analysis: Message Passing Algorithms and Sharp Asymptotics
• The Noise-Sensitivity Phase Transition in Compressed Sensing
• The LASSO risk for gaussian matrices
• Message Passing Algorithms for Compressed Sensing: II. Analysis and Validation
• Near-Optimal Coding for Many-user Multiple Access Channels
• Label-Imbalanced and Group-Sensitive Classification under Overparameterization
• On Convergence of the Alternating Projection Method for Matrix Completion and Sparse Recovery Problems
• The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
• Image Compression Based on Compressive Sensing: End-to-End Comparison with JPEG
• Online compressed sensing
• Bayesian compressed sensing with new sparsity-inducing prior
• Phase diagram of matrix compressed sensing
• Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals
• Semi-Blind Cascaded Channel Estimation for Reconfigurable Intelligent Surface Aided Massive MIMO
• Approximate Leave-One-Out for High-Dimensional Non-Differentiable Learning Problems
• Deep Learning Techniques for Inverse Problems in Imaging
• Empirical Bayes and Full Bayes for Signal Estimation
• TARM: A Turbo-type Algorithm for Affine Rank Minimization
• Universality in Learning from Linear Measurements
• Approximate Message Passing with Nearest Neighbor Sparsity Pattern Learning
• A rigorous geometry-probability equivalence in characterization of ${\ell }_1$-optimization
• On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling
• Blind Calibration in Compressed Sensing using Message Passing Algorithms
• Support Recovery with Sparsely Sampled Free Random Matrices
• Compressed Sensing via Universal Denoising and Approximate Message Passing
• Counterexamples to the Low-Degree Conjecture
• Approximate Message Passing with Parameter Estimation for Heavily Quantized Measurements
• EXIT Chart Analysis of Turbo Compressed Sensing Using Message Passing De-Quantization
• Non-Common Band SAR Interferometry via Compressive Sensing
• Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization
• Gaussian Approximation of Quantization Error for Estimation from Compressed Data
• Robust Group Synchronization via Cycle-Edge Message Passing
• Precoding via Approximate Message Passing with Instantaneous Signal Constraints
• Maximin Analysis of Message Passing Algorithms for Recovering Block Sparse Signals
• Optimization-based AMP for Phase Retrieval: The Impact of Initialization and ${\ell }_2$-regularization
• Layered Belief Propagation for Low-complexity Large MIMO Detection Based on Statistical Beams
• Self-Averaging Expectation Propagation
• Greedy Algorithms for Hybrid Compressed Sensing
• Algorithms for the Iterative Estimation of Discrete-Valued Sparse Vectors
• Multi-Processor Approximate Message Passing Using Lossy Compression
• DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds
• Fixed-Symbol Aided Random Access Scheme for Machine-to-Machine Communications
• On Compressed Sensing of Binary Signals for the Unsourced Random Access Channel
• Deep Neural Network Based Active User Detection for Grant-free NOMA Systems
• Bayes-Optimal Estimation in Generalized Linear Models via Spatial Coupling
• Temporal-Structure-Assisted Gradient Aggregation for Over-the-Air Federated Edge Learning
• Two-Part Reconstruction with Noisy-Sudocodes
• Scalable Approximations of Marginal Posteriors in Variable Selection
• Thresholds of descending algorithms in inference problems
• Fixed Points of Generalized Approximate Message Passing with Arbitrary Matrices
• Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis
• Bayesian Optimal Approximate Message Passing to Recover Structured Sparse Signals
• Simultaneous Active and Passive Information Transfer for RIS-Aided MIMO Systems: Iterative Decoding and Evolution Analysis
• Complex Trainable ISTA for Linear and Nonlinear Inverse Problems
• Compressed sensing with sparse, structured matrices
• Compressive neural representation of sparse, high-dimensional probabilities
• Overcoming The Limitations of Phase Transition by Higher Order Analysis of Regularization Techniques
• Prediction Errors for Penalized Regressions based on Generalized Approximate Message Passing
• Streaming Bayesian inference: theoretical limits and mini-batch approximate message-passing
• Blind Sensor Calibration using Approximate Message Passing
• Understanding Deep MIMO Detection
• Generalized Approximate Message Passing for Cosparse Analysis Compressive Sensing
• An Information-Percolation Bound for Spin Synchronization on General Graphs
• Mismatched Data Detection in Massive MU-MIMO
• The geometry of least squares in the 21st century
• Gardner formula for Ising perceptron models at small densities
• Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization
• Sharp Asymptotics and Optimal Performance for Inference in Binary Models
• Achieving Maximum-likelihood Detection Performance with Square-order Complexity in Large Quasi-Symmetric MIMO Systems
• Approximate Message Passing under Finite Alphabet Constraints
• Approximate Message Passing with Rigorous Guarantees for Pooled Data and Quantitative Group Testing
• Sparse Bayesian Learning Approach for Discrete Signal Reconstruction
• Exploring Weight Importance and Hessian Bias in Model Pruning
• Bayesian Hypothesis Test using Nonparametric Belief Propagation for Noisy Sparse Recovery
• Capacity Optimality of AMP in Coded Systems
• Phase transition in the spiked random tensor with Rademacher prior
• Precise Error Analysis of the LASSO under Correlated Designs
• Consistent Risk Estimation in Moderately High-Dimensional Linear Regression
• Sample Distortion for Compressed Imaging
• Exact solution to the random sequential dynamics of a message passing algorithm
• An equivalence between high dimensional Bayes optimal inference and M-estimation
• Convolutional Sparse Support Estimator Network (CSEN) From energy efficient support estimation to learning-aided Compressive Sensing
• Sparse approximation problem: how rapid simulated annealing succeeds and fails
• Compressive Computed Tomography Reconstruction through Denoising Approximate Message Passing
• Restricted Isometry Random Variables: Probability Distributions, RIC Prediction and Phase Transition Analysis for Gaussian Encoders
• Almost Lossless Analog Signal Separation
• Multi-Branch Matching Pursuit with applications to MIMO radar
• Bilinear Generalized Vector Approximate Message Passing
• Application of compressed sensing to genome wide association studies and genomic selection
• Evaluation of Generalized Degrees of Freedom for Sparse Estimation by Replica Method
• Group Testing with Side Information via Generalized Approximate Message Passing
• Equivalence between algorithmic instability and transition to replica symmetry breaking in perceptron learning systems
• Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
• TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems
• Optimal Data Detection and Signal Estimation in Systems with Input Noise
• Out-of-sample error estimate for robust M-estimators with convex penalty
• Low-Complexity Blind Parameter Estimation in Wireless Systems with Noisy Sparse Signals
• Soft Interference Cancellation for Random Coding in Massive Gaussian Multiple-Access
• Memory Approximate Message Passing
• Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
• Joint User Identification, Channel Estimation, and Signal Detection for Grant-Free NOMA
• Spectral Method for Phase Retrieval: an Expectation Propagation Perspective
• A Model-Driven Deep Learning Network for MIMO Detection
• Inference in Multi-Layer Networks with Matrix-Valued Unknowns
• Statistical Physics and Information Theory Perspectives on Linear Inverse Problems
• Factorized Graph Representations for Semi-Supervised Learning from Sparse Data
• Generalized Expectation Consistent Signal Recovery for Nonlinear Measurements
• Performance Trade-Offs in Multi-Processor Approximate Message Passing
• Boolean Matrix Factorization and Noisy Completion via Message Passing
• Multi-Resolution Compressed Sensing via Approximate Message Passing
• Properties of spatial coupling in compressed sensing
• Distributed Approximate Message Passing for Compressed Sensing
• A Max-Product EM Algorithm for Reconstructing Markov-tree Sparse Signals from Compressive Samples
• Convolutional Neural Associative Memories: Massive Capacity with Noise Tolerance
• Hamming Compressed Sensing
• Phase transition in compressed sensing with horseshoe prior
• Joint Channel-and-Data Estimation for Large-MIMO Systems with Low-Precision ADCs
• Detangling robustness in high dimensions: composite versus model-averaged estimation
• Sparse Bayesian Learning Using Approximate Message Passing with Unitary Transformation
• Neural-prior stochastic block model
• A Probabilistic Bayesian Approach to Recover $R_2^{\ast }$ map and Phase Images for Quantitative Susceptibility Mapping
• Noisy Pooled PCR for Virus Testing
• Semi-analytic approximate stability selection for correlated data in generalized linear models
• Analysis of Democratic Voting Principles used in Distributed Greedy Algorithms
• ${\ell }_1$-penalized Multinomial Regression: Estimation, inference, and prediction, with an application to risk factor identification for different dementia subtypes
• Analysis of Random Sequential Message Passing Algorithms for Approximate Inference
• Efficient Massive Machine Type Communication (mMTC) via AMP
• Approximate Message Passing for Indoor THz Channel Estimation
• Optimal Trade-offs in Multi-Processor Approximate Message Passing
• Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework
• Bayesian reconstruction of memories stored in neural networks from their connectivity
• Scampi: a robust approximate message-passing framework for compressive imaging
• Binary Sparse Bayesian Learning Algorithm for One-bit Compressed Sensing
• Optimum GSSK Transmission in Massive MIMO Systems Using the Box-LASSO Decoder
• Binary Matrix Factorization via Dictionary Learning
• On Sparse Vector Recovery Performance in Structurally Orthogonal Matrices via LASSO
• Bounds on restricted isometry constants of random matrices
• Estimator of Prediction Error Based on Approximate Message Passing for Penalized Linear Regression
• Joint Beamforming and Compressed Sensing for Uplink Grant-Free Access
• Minimum ${\ell }_1$-norm interpolators: Precise asymptotics and multiple descent
• Compressed sensing with l0-norm: statistical physics analysis and algorithms for signal recovery
• Message passing-based joint CFO and channel estimation in millimeter wave systems with one-bit ADCs
• Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective
• Exact high-dimensional asymptotics for Support Vector Machine
• Low-Rank Matrix Completion: A Contemporary Survey
• Cooperative Learning via Federated Distillation over Fading Channels
• Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation
• Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO
• A signal recovery algorithm for sparse matrix based compressed sensing
• Computing Estimators of Dantzig Selector type via Column and Constraint Generation
• Sparse-promoting Full Waveform Inversion based on Online Orthonormal Dictionary Learning
• Robust Activity Detection for Massive Random Access
• Fast Signal Separation of 2D Sparse Mixture via Approximate Message-Passing
• Empirical Bayes PCA in high dimensions
• Hardware Implementation of Compressed Sensing based Low Complex Video Encoder
• Efficient Designs of SLOPE Penalty Sequences in Finite Dimension
• Computationally Efficient Sparse Bayesian Learning via Generalized Approximate Message Passing
• Critical Behavior and Universality Classes for an Algorithmic Phase Transition in Sparse Reconstruction
• High-Dimensional CSI Acquisition in Massive MIMO: Sparsity-Inspired Approaches
• Learning based signal detection for MIMO systems with unknown noise statistics
• Understanding the Under-Coverage Bias in Uncertainty Estimation
• Performance Analysis of Cell-Free Massive MIMO Systems with Massive Connectivity
• On the Cryptographic Hardness of Learning Single Periodic Neurons
• Signal Recovery on Incoherent Manifolds
• Detection-Directed Sparse Estimation using Bayesian Hypothesis Test and Belief Propagation
• A Non-Binary Associative Memory with Exponential Pattern Retrieval Capacity and Iterative Learning: Extended Results
• Phase transition in binary compressed sensing based on $L_1$-norm minimization
• Sparse Signal Recovery using Generalized Approximate Message Passing with Built-in Parameter Estimation
• Jointly Sparse Signal Recovery and Support Recovery via Deep Learning with Applications in MIMO-based Grant-Free Random Access
• Vector Approximate Message Passing Algorithm for Structured Perturbed Sensing Matrix
• Regularization by Denoising: Clarifications and New Interpretations
• A Unified Framework of State Evolution for Message-Passing Algorithms
• Online unsupervised deep unfolding for MIMO channel estimation
• An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression
• Scalable Deep Compressive Sensing
• Structure Adaptive Elastic-Net
• The planted XY model: thermodynamics and inference
• Generalized Approximate Survey Propagation for High-Dimensional Estimation
• An Overview of Multi-Processor Approximate Message Passing
• Asymptotic MMSE Analysis Under Sparse Representation Modeling
• Generalization Error of Generalized Linear Models in High Dimensions
• Optimization of the Belief-Propagation Algorithm for Distributed Detection by Linear Data-Fusion Techniques
• Sparse Message Passing Based Preamble Estimation for Crowded M2M Communications
• Belief Propagation Methods for Intercell Interference Coordination
• Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokens
• Approximate Message Passing in Coded Aperture Snapshot Spectral Imaging
• Estimation for High-Dimensional Multi-Layer Generalized Linear Model -- Part I: The Exact MMSE Estimator
• Analysis of Approximate Message Passing with a Class of Non-Separable Denoisers
• Towards a better compressed sensing
• On Massive IoT Connectivity with Temporally-Correlated User Activity
• The Limiting Poisson Law of Massive MIMO Detection with Box Relaxation
• Optimal Number of Measurements in a Linear System with Quadratically Decreasing SNR
• Wiener Filters in Gaussian Mixture Signal Estimation with Infinity-Norm Error
• Multiprocessor Approximate Message Passing with Column-Wise Partitioning
• Learning Cluster Structured Sparsity by Reweighting
• Modified Hard Thresholding Pursuit with Regularization Assisted Support Identification
• Fully Convolutional Measurement Network for Compressive Sensing Image Reconstruction
• Sparsity/Undersampling Tradeoffs in Anisotropic Undersampling, with Applications in MR Imaging/Spectroscopy
• Blind calibration for compressed sensing: State evolution and an online algorithm
• Optimization for Compressed Sensing: the Simplex Method and Kronecker Sparsification
• Asymptotic Performance Prediction for ADMM-Based Compressed Sensing
• Scalable Uplink Signal Detection in C-RANs via Randomized Gaussian Message Passing
• Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries
• Blind Signal Detection in Massive MIMO: Exploiting the Channel Sparsity
• Message Passing in C-RAN: Joint User Activity and Signal Detection
• Multi-Level Error-Resilient Neural Networks with Learning
• A Novel Sum-Product Detection Algorithm for Faster-than-Nyquist Signaling: A Deep Learning Approach
• Feature-Aided Adaptive-Tuning Deep Learning for Massive Device Detection
• Bayes-Optimal Convolutional AMP
• Deep-Learned Approximate Message Passing for Asynchronous Massive Connectivity
• Minimum Complexity Pursuit for Universal Compressed Sensing
• Orthogonal Sparse Superposition Codes for Ultra-Reliable Low-Latency Communications
• Block Compressed Sensing Based Distributed Device Detection for M2M Communications
• Replicated Vector Approximate Message Passing For Resampling Problem
• Mismatched Estimation in Large Linear Systems
• Bernoulli-Gaussian Approximate Message-Passing Algorithm for Compressed Sensing with 1D-Finite-Difference Sparsity
• The phase diagram of compressed sensing with ${\ell }_0$-norm regularization
• Semi-Blind Channel-and-Signal Estimation for Uplink Massive MIMO With Channel Sparsity
• A Survey on Nonconvex Regularization Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning
• PIPO-Net: A Penalty-based Independent Parameters Optimization Deep Unfolding Network
• CS-VQA: Visual Question Answering with Compressively Sensed Images
• Fast Fourier-Based Generation of the Compression Matrix for Deterministic Compressed Sensing
• Accelerating Cross-Validation in Multinomial Logistic Regression with ${\ell }_1$-Regularization
• A Covariance-based User Activity Detection and Channel Estimation Approach with Novel Pilot Design
• Decision Triggered Data Transmission and Collection in Industrial Internet of Things
• Distributed Video Adaptive Block Compressive Sensing
• Low noise sensitivity analysis of Lq-minimization in oversampled systems
• Generating Functional Analysis for Iterative CDMA Multiuser Detectors
• Precise Performance Analysis of the LASSO under Matrix Uncertainties
• Algorithm Unfolding for Block-sparse and MMV Problems with Reduced Training Overhead
• An Analysis of State Evolution for Approximate Message Passing with Side Information
• Belief-propagation-based joint channel estimation and decoding for spectrally efficient communication over unknown sparse channels
• Gaussian Message Passing for Overloaded Massive MIMO-NOMA
• Generalized Approximate Message Passing for Massive MIMO mmWave Channel Estimation with Laplacian Prior
• Random Access for Massive Machine-Type Communications
• Deep Learning Assisted User Identification in Massive Machine-Type Communications
• Precise Error Rates for Computationally Efficient Testing
• Meta Learning-based MIMO Detectors: Design, Simulation, and Experimental Test
• Sparse linear regression -- CLuP achieves the ideal \emph{exact} ML
• VLSI Friendly Framework for Scalable Video Coding based on Compressed Sensing
• Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli
• Sparse Vector Recovery: Bernoulli-Gaussian Message Passing
• Analysis of Approximate Message Passing with Non-Separable Denoisers and Markov Random Field Priors
• AMPA-Net: Optimization-Inspired Attention Neural Network for Deep Compressed Sensing
• Nonlinear Function Estimation with Empirical Bayes and Approximate Message Passing
• VLSI Design of a Nonparametric Equalizer for Massive MU-MIMO
• An Approach to Complex Bayesian-optimal Approximate Message Passing
• Optimizing Binary Symptom Checkers via Approximate Message Passing
• Replica Analysis for Generalized Linear Regression with IID Row Prior
• Sharp global convergence guarantees for iterative nonconvex optimization: A Gaussian process perspective
• Structured sublinear compressive sensing via belief propagation
• Compressed Coding, AMP Based Decoding and Analog Spatial Coupling
• Universality of Approximate Message Passing Algorithms
• The Sampling Rate-Distortion Tradeoff for Sparsity Pattern Recovery in Compressed Sensing
• On the Minimax Risk of Dictionary Learning
• Rigorous State Evolution Analysis for Approximate Message Passing with Side Information
• Random linear systems with sparse solutions -- asymptotics and large deviations
• Efficient ${\ell }_q$ Minimization Algorithms for Compressive Sensing Based on Proximity Operator
• Symbol Detection for Massive MIMO AF Relays Using Approximate Bayesian Inference
• Box constrained ${\ell }_1$ optimization in random linear systems -- finite dimensions
• Box constrained ${\ell }_1$ optimization in random linear systems -- asymptotics
• Random linear under-determined systems with block-sparse solutions -- asymptotics, large deviations, and finite dimensions
• Partial ${\ell }_1$ optimization in random linear systems -- phase transitions and large deviations
• Compressed sensing and optimal denoising of monotone signals
• Planted matching problems on random hypergraphs
• Power Allocation in Compressed Sensing of Non-uniformly Sparse Signals
• Algebra of L-banded Matrices
• Insense: Incoherent Sensor Selection for Sparse Signals
• Denoising-based Turbo Compressed Sensing
• The Complete Lasso Tradeoff Diagram
• Efficient and Robust Recovery of Sparse Signal and Image Using Generalized Nonconvex Regularization
• Design and Analysis of a Greedy Pursuit for Distributed Compressed Sensing
• On Compressive Sensing in Coding Problems: A Rigorous Approach
• A Bayesian approach to sparse channel estimation in OFDM systems
• A Signal Processor for Gaussian Message Passing
• Bipartite Graph based Construction of Compressed Sensing Matrices
• Local Convergence of an AMP Variant to the LASSO Solution in Finite Dimensions
• Expectation propagation on the diluted Bayesian classifier
• SPARC-LDPC Coding for MIMO Massive Unsourced Random Access
• SUREMap: Predicting Uncertainty in CNN-based Image Reconstruction Using Stein's Unbiased Risk Estimate
• Universally Elevating the Phase Transition Performance of Compressed Sensing: Non-Isometric Matrices are Not Necessarily Bad Matrices
• Verification-Based Interval-Passing Algorithm for Compressed Sensing
• Many-User Multiple Access with Random User Activity: Achievability Bounds and Efficient Schemes
• Linear under-determined systems with sparse solutions: Redirecting a challenge?
• Fundamental limits and algorithms for sparse linear regression with sublinear sparsity
• On Simplicity and Complexity in the Brave New World of Large-Scale Neuroscience
• From compression to compressed sensing
• LASSO risk and phase transition under dependence
• Symbol Detection for Coarsely Quantized OTFS
• Optimal thresholds and algorithms for a model of multi-modal learning in high dimensions
• Characterizing the SLOPE Trade-off: A Variational Perspective and the Donoho-Tanner Limit
• Contact Tracing Information Improves the Performance of Group Testing Algorithms
• Subsampling at Information Theoretically Optimal Rates
• Asymptotic Statistical Analysis of Sparse Group LASSO via Approximate Message Passing Algorithm
• Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems
• Linear Operator Approximate Message Passing (OpAMP)
• Signal reconstruction in linear mixing systems with different error metrics
• Exact Sparse Recovery with L0 Projections
• Message Passing Algorithm for Distributed Downlink Regularized Zero-forcing Beamforming with Cooperative Base Stations
• Mixture Gaussian Signal Estimation with L_infty Error Metric
• JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging
• RLS Recovery with Asymmetric Penalty: Fundamental Limits and Algorithmic Approaches