Stable signal recovery from incomplete and inaccurate measurements

2006/03/01 by Emmanuel J. Candès, Justin K. Romberg, Justin Romberg +1 · 7,189 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Combinatorics #Compressed sensing #Computer science #Gaussian #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Pure mathematics #Regularization (linguistics) #Row #Sparse and Compressive Sensing Techniques #Term (time)

paper · doi:10.1002/cpa.20124

published in Communications on Pure and Applied Mathematics 59(8), 1207-1223 (Wiley)

openalex publication_date 2006/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Abstract Suppose we wish to recover a vector x 0 ∈ ℝ 𝓂 (e.g., a digital signal or image) from incomplete and contaminated observations y = A x 0 + e ; A is an 𝓃 × 𝓂 matrix with far fewer rows than columns (𝓃 ≪ 𝓂) and e is an error term. Is it possible to recover x 0 accurately based on the data y ? To recover x 0 , we consider the solution x # to the 𝓁 1 ‐regularization problem where ϵ is the size of the error term e . We show that if A obeys a uniform uncertainty principle (with unit‐normed columns) and if the vector x 0 is sufficiently sparse, then the solution is within the noise level As a first example, suppose that A is a Gaussian random matrix; then stable recovery occurs for almost all such A 's provided that the number of nonzeros of x 0 is of about the same order as the number of observations. As a second instance, suppose one observes few Fourier samples of x 0 ; then stable recovery occurs for almost any set of 𝓃 coefficients provided that the number of nonzeros is of the order of 𝓃/(log 𝓂) 6 . In the case where the error term vanishes, the recovery is of course exact, and this work actually provides novel insights into the exact recovery phenomenon discussed in earlier papers. The methodology also explains why one can also very nearly recover approximately sparse signals. © 2006 Wiley Periodicals, Inc.

Cited by

• Recovering Compressively Sampled Signals Using Partial Support Information
• First-Principles Lattice Dynamics Method for Strongly Anharmonic Crystals
• Quantum sensing
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• The Dantzig selector: Statistical estimation when p is much larger than n
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• ST-DDA: Dynamic Channel Estimation in the Doppler-Delay-Angle Domain via Sparse Subspace Tracking for TDD Systems
• Accelerated Stochastic Zeroth-Order Quasar-Convex Optimization
• Sparse Approximation by Semidefinite Programming
• NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes
• Stable and robust ℓ_p-constrained compressive sensing recovery via robust width property
• Preconditioned training of normalizing flows for variational inference in inverse problems
• Compressive Sampling Using EM Algorithm
• Robust Recovery of Signals From a Structured Union of Subspaces
• Non-submodular Function Maximization subject to a Matroid Constraint, with Applications
• Sparse System Identification in Pairs of FIR and TM Bases
• Joint Beam Training and Positioning For Intelligent Reflecting Surfaces Assisted Millimeter Wave Communications
• Regularization in High-Dimensional Regression and Classification via\n Random Matrix Theory
• Deep Sparse Coding Using Optimized Linear Expansion of Thresholds
• A general framework of rotational sparse approximation in uncertainty quantification
• An inverse problem for the wave equation with one measurement and the pseudorandom noise
• Segment-Sliding Reconstruction of Pulsed Radar Echoes with Sub-Nyquist Sampling
• Probabilistic Recovery Guarantees for Sparsely Corrupted Signals
• On the ℓ^∞-norms of the Singular Vectors of Arbitrary Powers of a Difference Matrix with Applications to Sigma-Delta Quantization
• CT Image Reconstruction in a Low Dimensional Manifold
• Hidden cliques and the certification of the restricted isometry property
• Compressed Sensing with Deep Image Prior and Learned Regularization
• Nonlinear frames and sparse reconstructions in Banach spaces
• Stochastic collocation methods via minimization of Transformed L₁ penalty
• Insight into Primal Augmented Lagrangian Multilplier Method
• Extension of Sparse Randomized Kaczmarz Algorithm for Multiple\n Measurement Vectors
• Weak Stability of ℓ₁-minimization Methods in Sparse Data Reconstruction
• Phase-space entropy at acquisition reflects downstream learnability
• Deep Learning-Guided Image Reconstruction from Incomplete Data
• Do Generalized-Gamma Scale Mixtures of Normals Fit Large Image Datasets?
• Ramanujan sums in signal recovery and uncertainty principle inequalities
• From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification
• Towards Machine Intelligence
• On the Iterative Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing
• PySensors: A Python Package for Sparse Sensor Placement
• Rates and architectures for learning geometrically non-trivial operators
• Fast L1-L2 minimization via a proximal operator
• Large-aperture computational single-sensor microwave imager using 1-bit programmable coding metasurface at single frequency
• Adaptive sampling using variational autoencoder and reinforcement learning
• Multichannel group sparsity methods for compressive channel estimation in doubly selective multicarrier MIMO systems (extended version)
• Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit
• Bayesian Massive MIMO Channel Estimation with Parameter Estimation Using Low-Resolution ADCs
• Compressed Sensing using Generative Models
• Solving Tall Dense Linear Programs in Nearly Linear Time
• Compressed sensing in the quaternion algebra
• Compressive Spectrum Sensing for Cognitive Radio Networks
• Sparse regression with highly correlated predictors
• Universal Rate-Efficient Scalar Quantization
• cryoSENSE: Compressive Sensing Enables High-throughput Microscopy with Sparse and Generative Priors on the Protein Cryo-EM Image Manifold
• Spectrum of normal operators that generate certain scalable iterative systems
• Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator
• An Optimal Algorithm for l1-Heavy Hitters in Insertion Streams and Related Problems
• Random Search Algorithms for the Sparse Null Vector Problem
• Sparse stabilization of mean-field agent dynamics through a three-operator splitting method
• All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation
• Sparse Recovery by Non-convex Optimization -- Instance Optimality
• A problem dependent analysis of SOCP algorithms in noisy compressed sensing
• Exclusive Group Lasso for Structured Variable Selection
• Bayesian Compressed Regression
• Optimization landscape of ℓ₀-Bregman relaxations
• Constrained Shadow Tomography for Molecular Simulation on Quantum Devices
• How to generate accurate continuous thermal regimes from sparse but regular temperature measurements
• Plug-and-Play Algorithms for Large-scale Snapshot Compressive Imaging
• Reconstruction of Ordinary Differential Equations From Time Series Data
• Adaptive Restart for Accelerated Gradient Schemes
• Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalent
• Bayesian compressed sensing with new sparsity-inducing prior
• An efficient proximal algorithm for squared L1 over L2 regularized sparse recovery
• Atomic norm denoising with applications to line spectral estimation
• Some smooth divergences for ℓ₁-approximations
• Refined additive uncertainty principle
• L₁-norm Regularized Indefinite Kernel Logistic Regression
• Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere
• Weighed l1 on the simplex: Compressive sensing meets locality
• A performance analysis framework for SOCP algorithms in noisy compressed sensing
• Random Subdictionaries and Coherence Conditions for Sparse Signal Recovery
• Suprema of Chaos Processes and the Restricted Isometry Property
• InstaHide: Instance-hiding Schemes for Private Distributed Learning
• 1-Bit Compressive Sensing for Efficient Federated Learning Over the Air
• Minimization of Transformed L₁ Penalty: Closed Form Representation and Iterative Thresholding Algorithms
• Support Recovery of Sparse Signals
• No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis
• On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions
• Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames
• An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]
• Single-pixel imaging via compressive sampling
• Atomic Norm Denoising With Applications to Line Spectral Estimation
• Leveraging Diversity and Sparsity in Blind Deconvolution
• Iterative hard thresholding for compressed sensing
• Robust sparse recovery with sparse Bernoulli matrices via expanders
• Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraints
• L1-norm minimization for quaternion signals
• A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
• Eigenmatrix for unstructured sparse recovery
• Constant-Expansion Suffices for Compressed Sensing with Generative Priors
• Algebraic compressed sensing
• Compressed sensing for body MRI
• Adaptive compressed sensing - a new class of self-organizing coding models for neuroscience
• Optimal RIP bounds for sparse signals recovery via ℓ minimization
• Recovery of signals under the condition on RIC and ROC via prior support information
• Stability results for random sampling of sparse trigonometric polynomials
• Optimized Compressed Sensing via Incoherent Frames Designed by Convex Optimization
• A Theoretical Analysis of Sparse Recovery Stability of Dantzig Selector and LASSO
• Achieving the Scaling Law of SNR-Monitoring in Dynamic Wireless Networks
• Exact Reconstruction using Beurling Minimal Extrapolation
• Improving Network Slimming with Nonconvex Regularization
• New analysis of manifold embeddings and signal recovery from compressive measurements
• Fast Image Recovery Using Variable Splitting and Constrained Optimization
• A Dual Symmetric Gauss-Seidel Alternating Direction Method of Multipliers for Hyperspectral Sparse Unmixing
• Convergence of a Relaxed Variable Splitting Coarse Gradient Descent Method for Learning Sparse Weight Binarized Activation Neural Networks
• Computational methods for large-scale inverse problems: a survey on hybrid projection methods
• Limited Tomography Reconstruction via Tight Frame and Sinogram Extrapolation
• Balanced conic rectified flow
• Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization
• Image Block Loss Restoration Using Sparsity Pattern as Side Information
• Instance optimality in phase retrieval
• Efficient Representations of Signals in Nonlinear Signal Processing with Applications to Inverse Problems
• One-bit compressive sensing with norm estimation
• Design and Analysis of a Greedy Pursuit for Distributed Compressed Sensing
• Joint Signal Recovery and Uncertainty Quantification via the Residual Prior Transform
• Multi-Label Prediction via Compressed Sensing
• A Convexly Constrained LiGME Model and Its Proximal Splitting Algorithm
• Subspace Pursuit for Compressive Sensing Signal Reconstruction
• Majority Vote Compressed Sensing
• Super-resolution by means of Beurling minimal extrapolation
• Guarantees for Greedy Maximization of Non-submodular Functions with Applications
• Purified phase estimation samples spectra efficiently
• Performance Analysis of Spectral Clustering on Compressed, Incomplete and Inaccurate Measurements
• Exploiting Model Sparsity in Adaptive MPC: A Compressed Sensing Viewpoint
• Recovery of Integer Images from Minimal DFT Measurements: Uniqueness and Inversion Algorithms
• Simple Bounds for Noisy Linear Inverse Problems with Exact Side Information
• Simplifying Optimal Transport through Schatten-p Regularization
• Do Subsampled Newton Methods Work for High-Dimensional Data?
• Sparse Phase Retrieval: Convex Algorithms and Limitations
• Matrix-free Interior Point Method for Compressed Sensing Problems
• Density Evolution Analysis of Node-Based Verification-Based Algorithms in Compressive Sensing
• Analysis of Democratic Voting Principles used in Distributed Greedy Algorithms
• Universality in Learning from Linear Measurements
• Multivariate sparse interpolation using randomized Kronecker substitutions
• Estimation in exponential family Regression based on linked data contaminated by mismatch error
• Quantum Sparse Recovery and Quantum Orthogonal Matching Pursuit
• Rare-Allele Detection Using Compressed Se(que)nsing
• Task Vectors, Learned Not Extracted: Performance Gains and Mechanistic Insight
• Multi-Processor Approximate Message Passing Using Lossy Compression
• Non-convex Fraction Function Penalty: Sparse Signals Recovered from Quasi-linear Systems
• Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0<q⩽1
• Sharp RIP bound for sparse signal and low-rank matrix recovery
• Recovery analysis for weighted ℓ1-minimization using the null space property
• Projection & Probability-Driven Black-Box Attack
• Efficient iterative thresholding algorithms with functional feedbacks and convergence analysis
• Compressive Sensing with Local Geometric Features
• A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm
• Super-Resolution of Brain MRI Images using Overcomplete Dictionaries and Nonlocal Similarity
• Deep(er) Learning
• Inverse Potential Problems for Divergence of Measures with Total Variation Regularization
• Pixelated Butterfly: Simple and Efficient Sparse training for Neural Network Models
• Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection
• Super-resolution techniques to simulate electronic spectra of large molecular systems
• Exact recoverability from dense corrupted observations via L₁ minimization
• The Fourier ratio: A unifying measure of complexity for recovery, localization, and learning
• Learning Mixtures of Sparse Linear Regressions Using Sparse Graph Codes
• Sparsity in time-frequency representations
• A simple proof that random matrices are democratic
• PARNES: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals
• Sparse Legendre expansions via ℓ₁ minimization
• Mixed Operators in Compressed Sensing
• Fast L1-Minimization Algorithms For Robust Face Recognition
• Multidimensional Chebyshev spaces, hierarchy of infinite-dimensional spaces and Kolmogorov-Gelfand widths
• Clustered Sparsity and Separation of Cartoon and Texture
• A Scale Invariant Approach for Sparse Signal Recovery
• Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
• On Maximization of Weakly Modular Functions: Guarantees of Multi-stage Algorithms, Tractability, and Hardness
• Compressive Sensing of Color Images Using Nonlocal Higher Order Dictionary
• Iterative Hard Thresholding for Compressed Sensing
• Low rank matrix recovery from Clifford orbits
• A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation
• Sparsity estimation in compressive sensing with application to MR images
• PySensors 2.0: A Python Package for Sparse Sensor Placement
• Sparsity Lower Bounds for Dimensionality Reducing Maps
• High-Quality Tomographic Image Reconstruction Integrating Neural Networks and Mathematical Optimization
• Convolutional Dictionary Learning in Hierarchical Networks
• Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance
• Lower Bounds for Compressed Sensing with Generative Models
• Learning functions through Diffusion Maps
• Uniform uncertainty principle for Bernoulli and subgaussian ensembles
• Improved bounds for the RIP of Subsampled Circulant matrices
• On the Certification of the Restricted Isometry Property
• Stable Principal Component Pursuit
• Early Classification of Time Series is Meaningful
• MemeSequencer: Sparse Matching for Embedding Image Macros
• Functional Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem
• Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes
• Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing
• New Analysis of Manifold Embeddings and Signal Recovery from Compressive Measurements
• Learning Functions of Few Arbitrary Linear Parameters in High Dimensions
• Recovery Guarantees for Compressible Signals with Adversarial Noise
• Detection-Directed Sparse Estimation using Bayesian Hypothesis Test and Belief Propagation
• Structure-Blind Signal Recovery
• Highly robust error correction by convex programming
• Compressive Sensing over the Grassmann Manifold: a Unified Geometric Framework
• Cooperative Sparsity Pattern Recovery in Distributed Networks Via\n Distributed-OMP
• Polarization Reconfigurable Transmit-Receive Beam Alignment with Interpretable Transformer
• Nonuniqueness of Solutions of a Class of ℓ₀-minimization Problems
• Compressive sensing: a paradigm shift in signal processing
• A Sharp Condition for Exact Support Recovery of Sparse Signals With Orthogonal Matching Pursuit
• Compressive Sensing Based Opportunistic Protocol for Throughput Improvement in Wireless Networks
• Iterative ℓ₁ minimization for non-convex compressed sensing
• The Cramer-Rao Bound for Sparse Estimation
• Compressed Sensing: How sharp is the Restricted Isometry Property
• Random Sampling of Sparse Trigonometric Polynomials II - Orthogonal Matching Pursuit versus Basis Pursuit
• Bacterial Community Reconstruction Using A Single Sequencing Reaction
• A Unified Framework for Sparse Relaxed Regularized Regression: SR3
• High-dimensional robust regression and outliers detection with SLOPE
• Sparse Reconstruction via The Reed-Muller Sieve
• Lensless Compressive Imaging
• Inferring Rankings Using Constrained Sensing
• Insense: Incoherent Sensor Selection for Sparse Signals
• Multi-view in Lensless Compressive Imaging
• Networked Estimation using Sparsifying Basis Prediction
• Is "Compressed Sensing" compressive? Can it beat the Nyquist Sampling Approach?
• Large sparse signal recovery by conjugate gradient algorithm based on smoothing technique
• Sparse Stabilization and Control of Alignment Models
• Empirical average-case relation between undersampling and sparsity in x-ray CT
• Quantum Spectral Reasoning: A Non-Neural Architecture for Interpretable Machine Learning
• 1-Bit Compressive Sensing: Reformulation and RRSP-Based Sign Recovery Theory
• An Overview of Algorithms for Contactless Cardiac Feature Extraction from Radar Signals: Advances and Challenges
• Expressivity of expand-and-sparsify representations
• Optimal Schatten-q and Ky-Fan-k Norm Rate of Low Rank Matrix Estimation
• Compressive sensing Petrov-Galerkin approximation of high-dimensional\n parametric operator equations
• Optimal compressed sensing for mixing stochastic processes
• Subspace selection for projection maximization with matroid constraints
• Sparse Index Tracking Based On L_1/2 Model And Algorithm
• Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples
• On Detection-Directed Estimation Approach for Noisy Compressive Sensing
• Super-resolution using Sparse Representations over Learned Dictionaries: Reconstruction of Brain Structure using Electron Microscopy
• Robust Binary Fused Compressive Sensing using Adaptive Outlier Pursuit
• A null space analysis of the L1 synthesis method in dictionary-based compressed sensing
• Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting
• DOA Estimation via Optimal Weighted Low-Rank Matrix Completion
• Binary Fused Compressive Sensing: 1-Bit Compressive Sensing meets Group Sparsity
• Recovery of sparsest signals via ℓ^q-minimization
• Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators
• Compressive Time Delay Estimation Using Interpolation
• Application of compressed sensing to genome wide association studies and genomic selection
• Signal to Noise Ratio in Lensless Compressive Imaging
• PDF estimation for power grid systems via sparse regression
• Photoacoustic Reconstruction Using Sparsity in Curvelet Frame: Image versus Data Domain
• A First-order Augmented Lagrangian Method for Compressed Sensing
• Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Rank-1 Robust Principal Component Analysis
• L1 penalized LAD estimator for high dimensional linear
• Parallel Calibration for Sensor Array Radio Interferometers
• CSMCNet: Scalable Video Compressive Sensing Reconstruction with Interpretable Motion Estimation
• Convergence bounds for nonlinear least squares and applications to tensor recovery
• On the Foundation of Sparse Sensing (Part I): Necessary and Sufficient Sampling Theory and Robust Remaindering Problem
• Empirical Bayesian Inference using Joint Sparsity
• Computational Complexity versus Statistical Performance on Sparse Recovery Problems
• Compressed Sensing from Phaseless Gaussian Measurements via Linear Programming in the Natural Parameter Space
• Frame-based Approach for Sparse Representation of Signal Decomposition and Reconstruction
• High SNR Consistent Compressive Sensing
• Blind calibration for compressed sensing by convex optimization
• Optimal Sample Complexity for Stable Matrix Recovery
• Faster Sparse Multivariate Polynomial Interpolation of Straight-Line Programs
• Efficient Image Reconstruction and Practical Decomposition for Dual-energy Computed Tomography
• Plug-and-Play Algorithms for Video Snapshot Compressive Imaging
• Stable image reconstruction using total variation minimization
• Learning to synthesize: splitting and recombining low and high spatial frequencies for image recovery
• Analysis of Recurrent Linear Networks for Enabling Compressed Sensing of\n Time-Varying Signals
• CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
• Restricted isometries for partial random circulant matrices
• Reconstruction of Sub-Nyquist Random Sampling for Sparse and Multi-Band Signals
• A Memristor-Based Optimization Framework for AI Applications
• Thresholded Lasso for high dimensional variable selection and statistical estimation
• Damping Noise-Folding and Enhanced Support Recovery in Compressed Sensing
• Dynamics of information diffusion and its applications on complex networks
• Reconstruction Error Bounds for Compressed Sensing under Poisson or Poisson-Gaussian Noise Using Variance Stabilization Transforms
• Automatic Modulation Recognition of PSK Signals with Sub-Nyquist Sampling Based on High Order Statistics
• Simultaneously Structured Models with Application to Sparse and Low-rank Matrices
• On sparse interpolation and the design of deterministic interpolation points
• Dual form Complementary Masking for Domain-Adaptive Image Segmentation
• A critical review of LASSO and its derivatives for variable selection under dependence among covariates
• Weighted Superimposed Codes and Constrained Integer Compressed Sensing
• On a hierarchy of infinite-dimensional spaces and related Kolmogorov-Gelfand widths
• Computational Complexity of Certifying Restricted Isometry Property
• A Non-Convex Optimization Technique for Sparse Blind Deconvolution -- Initialization Aspects and Error Reduction Properties
• Bayesian computation: a perspective on the current state, and sampling backwards and forwards
• Privacy-preserving Learning via Deep Net Pruning
• On Dimension-free Tail Inequalities for Sums of Random Matrices and Applications
• A Nonparametric Approach to Modeling Choice with Limited Data
• SRA: Fast Removal of General Multipath for ToF Sensors
• ℓ₁-minimization method for link flow correction
• Sparse Choice Models
• Structured sublinear compressive sensing via belief propagation
• Retraction-based first-order feasible methods for difference-of-convex programs with smooth inequality and simple geometric constraints
• Sharp Trade-Offs in High-Dimensional Inference via 2-Level SLOPE
• Additive combinatorics with a view towards computer science and cryptography: An exposition
• Multi-resolution Compressive Sensing Reconstruction
• Generator Surgery for Compressed Sensing
• 1-bit Localization Scheme for Radar using Dithered Quantized Compressed Sensing
• Semi-supervised Sparse Representation with Graph Regularization for Image Classification
• Recovering Compressively Sampled Signals Using Partial Support\n Information
• Dual-density-based reweighted ℓ₁-algorithms for a class of ℓ₀-minimization problems
• Convolutional Neural Networks Analyzed via Convolutional Sparse Coding
• Subspace Embeddings Under Nonlinear Transformations
• CS-MCNet:A Video Compressive Sensing Reconstruction Network with Interpretable Motion Compensation
• Exploiting Redundancy, Recurrence and Parallelism: How to Link Millions of Addresses with Ten Lines of Code in Ten Minutes
• Iterative Alpha Expansion for estimating gradient-sparse signals from linear measurements
• On the Complexity Analysis of the Primal Solutions for the Accelerated Randomized Dual Coordinate Ascent
• The high order block RIP condition for signal recovery
• Sparse recovery via nonconvex regularized M-estimators over ℓ_q-balls
• Compressive Spectral Estimation for Nonstationary Random Processes
• Matrix Recovery from Rank-One Projection Measurements via Nonconvex Minimization
• A new sparsity promoting residual transform operator for Lasso regression
• D2C: Diffusion-Denoising Models for Few-shot Conditional Generation
• Small-sample Brain Mapping: Sparse Recovery on Spatially Correlated Designs with Randomization and Clustering
• On the Conditions of Sparse Parameter Estimation via Log-Sum Penalty Regularization
• Sparse Fast Fourier Transform for Exactly and Generally K-Sparse Signals by Downsampling and Sparse Recovery
• Solving OSCAR regularization problems by proximal splitting algorithms
• Sharp MSE Bounds for Proximal Denoising
• Piecewise Sparse Recovery in Unions of Bases
• Truncated Linear Regression in High Dimensions
• Nonuniform Sparse Recovery with Subgaussian Matrices
• Reed Muller Sensing Matrices and the LASSO
• On sharp stable recovery from clipped and folded measurements
• Compressive sensing by white random convolution
• Algebraic Machine Learning
• Optimality Conditions for Cardinality-Constrained Programs and a SCA Method
• Non-Convex Compressed Sensing with Training Data
• First-Order Sparse Convex Optimization: Better Rates with Sparse Updates
• Modal Regression based Structured Low-rank Matrix Recovery for Multi-view Learning
• Learning Sparse Additive Models with Interactions in High Dimensions
• Necessary moment conditions for exact reconstruction via basis pursuit
• Approximating Sampled Sinusoids and Multiband Signals Using Multiband Modulated DPSS Dictionaries
• Performance Bounds for Vector Quantized Compressive Sensing
• Efficient and Robust Recovery of Sparse Signal and Image Using Generalized Nonconvex Regularization
• High Dimensional Linear Regression using Lattice Basis Reduction
• Learning hidden influences in large-scale dynamical social networks: A data-driven sparsity-based approach
• Optimal Sparse Output Feedback Control Design: a Rank Constrained Optimization Approach
• Recovery of signals under the condition on RIC and ROC via prior support information
• Generalized Energy Based Models
• Coherence of high-dimensional random matrices in a Gaussian case : application of the Chen-Stein method
• Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries
• A Novel Compressed Sensing Scheme for Photoacoustic Tomography
• Implicit Neural Representation-Based MRI Reconstruction Method with Sensitivity Map Constraints
• Resilient Optimal Estimation Using Measurement Prior
• Practical approximate projection schemes in greedy signal space methods
• A Nonconvex Nonsmooth Regularization Method for Compressed Sensing and Low-Rank Matrix Completion
• Thermal Property Microscopy with Compressive Sensing Frequency-Domain Thermoreflectance
• Energy-Efficient Sensor Censoring for Compressive Distributed Sparse Signal Recovery
• Sparse PSD approximation of the PSD cone
• MetaSketch: Wireless Semantic Segmentation by Metamaterial Surfaces
• Demodulating Subsampled Direct Sequence Spread Spectrum Signals using Compressive Signal Processing
• A New Performance Guarantee for Orthogonal Matching Pursuit Using Mutual Coherence
• A strong restricted isometry property, with an application to phaseless compressed sensing
• Efficient Hierarchical Bayesian Inference for Spatio-temporal Regression Models in Neuroimaging
• A low-rank tensor method to reconstruct sparse initial states for PDEs with Isogeometric Analysis
• Compressed Sensing over ℓ_p-balls: Minimax Mean Square Error
• Signal Recovery on Graphs: Fundamental Limits of Sampling Strategies
• Linear Convergence of Stochastic Iterative Greedy Algorithms with Sparse Constraints
• Thresholding-based Iterative Selection Procedures for Model Selection and Shrinkage
• Support driven reweighted ℓ₁ minimization
• Sparse Approximate Solutions to Max-Plus Equations with Application to Multivariate Convex Regression
• Locally Convex Sparse Learning over Networks
• Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine
• (1+eps)-approximate Sparse Recovery
• Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices
• Combining geometry and combinatorics: A unified approach to sparse signal recovery
• Phase Transitions and Cosparse Tomographic Recovery of Compound Solid\n Bodies from Few Projections
• Probabilistic Recovery of Multiple Subspaces in Point Clouds by Geometric lp Minimization
• From Symmetry to Geometry: Tractable Nonconvex Problems
• The recovery of complex sparse signals from few phaseless measurements
• Noise Analysis for Lensless Compressive Imaging
• Sparse Representation Classification via Screening for Graphs
• Distributed soft thresholding for sparse signal recovery
• Sparsification of Matrices and Compressed Sensing
• Variational Inference for Computational Imaging Inverse Problems
• K-Median Clustering, Model-Based Compressive Sensing, and Sparse Recovery for Earth Mover Distance
• A framework to characterize performance of LASSO algorithms
• Nonparametric sparsity and regularization
• Simple, Efficient, and Neural Algorithms for Sparse Coding
• Compressive Imaging of Subwavelength Structures
• Unique Reconstruction From Mean-Field Measurements
• Automatic Modulation Recognition of PSK Signals Using Nonuniform Compressive Samples Based on High Order Statistics
• GPS Signal Acquisition via Compressive Multichannel Sampling
• A Novel Compressive Sensing based Enhanced Multiplexing Scheme for MIMO System
• Sparse recovery for spherical harmonic expansions
• A Practical Study of Longitudinal Reference Based Compressed Sensing for MRI
• Restricted q-Isometry Properties Adapted to Frames for Nonconvex l_q-Analysis
• Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective
• Robust Sparse Phase Retrieval Made Easy
• On anisotropic non-Lipschitz restoration model: lower bound theory and convergent algorithm
• Analysis-by-Synthesis-based Quantization of Compressed Sensing Measurements
• A Remark on the Lasso and the Dantzig Selector
• Understanding the Performance Gap in Preference Learning: A Dichotomy of RLHF and DPO
• Robust Dequantized Compressive Sensing
• Combined modeling of sparse and dense noise for improvement of Relevance Vector Machine
• The recoverability limit for superresolution via sparsity
• Recovery Analysis for Weighted \ℓ₁-Minimization Using a Null Space\n Property
• Gradient Estimation with Simultaneous Perturbation and Compressive Sensing
• A Comparison of Clustering and Missing Data Methods for Health Sciences
• DB-KSVD: Scalable Alternating Optimization for Disentangling High-Dimensional Embedding Spaces
• Progressive versus Random Projections for Compressive Capture of Images, Lightfields and Higher Dimensional Visual Signals
• Fast and Accurate Algorithms for Re-Weighted L1-Norm Minimization
• Time Invariant Error Bounds for Modified-CS based Sparse Signal Sequence Recovery
• Analysis and algorithms for some compressed sensing models based on L1/L2 minimization
• Deep Representation with ReLU Neural Networks
• High-Dimensional Optimization in Adaptive Random Subspaces
• Primal-Dual Sequential Subspace Optimization for Saddle-point Problems
• On Collaborative Compressive Sensing Systems: The Framework, Design and Algorithm
• Surfing: Iterative optimization over incrementally trained deep networks
• The Trimmed Lasso: Sparsity and Robustness
• Sequential Interval Passing for Compressed Sensing
• Relax, no need to round: integrality of clustering formulations
• Blind One-Bit Compressive Sampling
• Distributed Quantization for Measurement of Correlated Sparse Sources over Noisy Channels
• Light-sheets and smart microscopy, an exciting future is dawning
• One-Bit Compressed Sensing by Greedy Algorithms
• Sparse Time-Frequency decomposition by dictionary learning
• Unsupervised Detection of Distribution Shift in Inverse Problems using Diffusion Models
• Restricted Eigenvalue Conditions on Subgaussian Random Matrices
• Fast and RIP-optimal transforms
• Multireference Alignment using Semidefinite Programming
• Dictionary Identification - Sparse Matrix-Factorisation via ℓ₁-Minimisation
• Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints
• 2022 Review of Data-Driven Plasma Science
• Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints
• Orthogonal Matching Pursuit with Tikhonov and Landweber Regularization
• Sharp Sufficient Conditions for Stable Recovery of Block Sparse Signals by Block Orthogonal Matching Pursuit
• Spatially regularized compressed sensing of diffusion MRI data
• On Model-Based RIP-1 Matrices
• On Convex Duality in Linear Inverse Problems
• Hamming Compressed Sensing
• Rank Awareness in Joint Sparse Recovery
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Sparsity and non-Euclidean embeddings
• Performance Guarantees of the Thresholding Algorithm for the Co-Sparse Analysis Model
• Orthogonal Matching Pursuit under the Restricted Isometry Property
• Stronger L2/L2 Compressed Sensing; Without Iterating
• Compressed Compressor
• Minimum Variance Estimation of a Sparse Vector within the Linear Gaussian Model: An RKHS Approach
• Sparse High-Dimensional Linear Regression. Algorithmic Barriers and a Local Search Algorithm
• Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices
• The finite steps of convergence of the fast thresholding algorithms with feedbacks
• Rényi Information Dimension: Fundamental Limits of Almost Lossless Analog Compression
• Beyond ℓ₁-norm minimization for sparse signal recovery
• Quantized Compressive Sensing
• Parameterless Optimal Approximate Message Passing
• On Recovery of Sparse Signals via ℓ₁ Minimization
• Data-based prediction and causality inference of nonlinear dynamics
• (Nearly) Sample-Optimal Sparse Fourier Transform in Any Dimension; RIPless and Filterless
• Applications of Compressed Sensing in Communications Networks
• Compressive sensing and truncated moment problems on spheres
• Compressed Remote Sensing of Sparse Objects
• Joint Detection and Super-Resolution Estimation of Multipath Signal Parameters Using Incremental Automatic Relevance Determination
• Sparse recovery based on q-ratio constrained minimal singular values
• Compressive Estimation of Doubly Selective Channels in Multicarrier Systems: Leakage Effects and Sparsity-Enhancing Processing
• Nonlinear regularization techniques for seismic tomography
• Weighted-ℓ₁ minimization with multiple weighting sets
• Multi-shot Echo Planar Imaging for accelerated Cartesian MR Fingerprinting: An alternative to conventional spiral MR Fingerprinting
• Quantized Iterative Hard Thresholding: Bridging 1-bit and High-Resolution Quantized Compressed Sensing
• Observability for Initial Value Problems with Sparse Initial Data
• Stability Analysis for a Class of Sparse Optimization Problems
• Sparse recovery guarantees for block orthogonal binary matrices constructed via Generalized Euler Squares
• LOGAN: Latent Optimisation for Generative Adversarial Networks
• Concurrent Encryption and Authentication for Wireless Networks using Compressed Sensing
• Optimal Sketching Bounds for Sparse Linear Regression
• A refined convergence analysis of pDCA_e with applications to simultaneous sparse recovery and outlier detection
• Spread spectrum for imaging techniques in radio interferometry
• On Finding a Subset of Healthy Individuals from a Large Population
• Spectral Compressive Sensing with Polar Interpolation
• Iterative Sparse Asymptotic Minimum Variance Based Approaches for Array Processing
• Spatio-temporal Compressed Sensing with Coded Apertures and Keyed\n Exposures
• Activelets: Wavelets for sparse representation of hemodynamic responses
• Structural mediation of human brain activity revealed by white-matter interpolation of fMRI
• Quantum process tomography of unitary and near-unitary maps
• Distributed Reconstruction from Compressive Measurements: Nonconvexity and Heterogeneity
• Robust Linear Regression via ℓ₀ Regularization
• Efficient sensing of von Kármán vortices using compressive sensing
• Inverse Problems Over Probability Measure Space
• Dualizable Shearlet Frames and Sparse Approximation
• Development of a fast electromagnetic beam blanker for compressed sensing in scanning transmission electron microscopy
• Compressed Sensing in Astronomy
• Sparse approximate solution of fitting surface to scattered points by MLASSO model
• Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing
• OMP Based Joint Sparsity Pattern Recovery Under Communication Constraints
• Near-optimal phase retrieval of sparse vectors
• Compressing measurements in quantum dynamic parameter estimation
• A note on practical approximate projection schemes in signal space methods
• Multilinear Compressive Learning with Prior Knowledge
• Compressive inverse scattering: II. Multi-shot SISO measurements with born scatterers
• Classification of Spatio-Temporal Data via Asynchronous Sparse Sampling: Application to Flow Around a Cylinder
• On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence
• Decoding from Pooled Data: Sharp Information-Theoretic Bounds
• Subspace metrics for multivariate dictionaries and application to EEG
• Magnetic Turbulence Spectra and Intermittency in the Heliosheath and in the Local Interstellar Medium
• Compressive Sensing of Sparse Tensors
• A data-independent distance to infeasibility for linear conic systems
• A geometrical stability condition for compressed sensing
• Sparse Approximate Solution of Partial Differential Equations
• Compressive sensing of signals generated in plastic scintillators in a novel J-PET instrument
• Scalable Data-Driven Basis Selection for Linear Machine Learning Interatomic Potentials
• Sparse linear regression from perturbed data
• Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models
• Radial velocity data analysis with compressed sensing techniques
• Performance Bounds on Sparse Representations Using Redundant Frames
• A Relaxation Argument for Optimization in Neural Networks and Non-Convex Compressed Sensing
• Robust sparse image reconstruction of radio interferometric observations with purify
• Sparse Subspace Clustering via Two-Step Reweighted L1-Minimization: Algorithm and Provable Neighbor Recovery Rates
• Unknown Sparsity in Compressed Sensing: Denoising and Inference
• Compressed sensing quantum process tomography for superconducting quantum gates
• Sparse dynamical Boltzmann machine for reconstructing complex networks with binary dynamics
• Uncertainty Principle and Sparse Reconstruction in Pairs of Orthonormal Rational Function Bases
• Reconstruction of Binary Functions and Shapes From Incomplete Frequency Information
• A remark about orthogonal matching pursuit algorithm
• Revealing physical interaction networks from statistics of collective dynamics
• Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements
• Minimizing L 1 over L 2 norms on the gradient
• Robust Maximization of Non-Submodular Objectives
• A Robust Time Series Model with Outliers and Missing Entries
• Accelerating Ultrafast Spectroscopy with Compressive Sensing
• ℓ1-Analysis minimization and generalized (co-)sparsity: When does recovery succeed?
• Compressive matched-field processing
• Compressed-sensing tomography for qudits in Hilbert spaces of non-power-of-two dimensions
• Channel-Optimized Vector Quantizer Design for Compressed Sensing\n Measurements
• Compressive Earth observatory: An insight from AIRS/AMSU retrievals
• Surveillance video processing using compressive sensing
• Radial-velocity fitting challenge
• Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property
• On the Noise Robustness of Simultaneous Orthogonal Matching Pursuit
• High-Dimensional Estimation of Structured Signals From Non-Linear Observations With General Convex Loss Functions
• Airborne Radar STAP using Sparse Recovery of Clutter Spectrum
• DUE: A Deep Learning Framework and Library for Modeling Unknown Equations
• Online Regularization of Complex-Valued Neural Networks for Structure Optimization in Wireless-Communication Channel Prediction
• Feature Clustering for Support Identification in Extreme Regions
• A note on the minimization of a Tikhonov functional with ℓ1-penalty
• Enhanced imaging of microcalcifications in digital breast tomosynthesis through improved image-reconstruction algorithms. [europepmc]
• Lensless wide-field fluorescent imaging on a chip using compressive decoding of sparse objects. [europepmc]
• Feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory. [europepmc]
• Metal artifact reduction in x-ray computed tomography (CT) by constrained optimization. [europepmc]
• A constrained, total-variation minimization algorithm for low-intensity x-ray CT. [europepmc]
• Characterization of statistical prior image constrained compressed sensing (PICCS): II. Application to dose reduction. [europepmc]
• Reverse engineering and identification in systems biology: strategies, perspectives and challenges. [europepmc]
• Reconstructing propagation networks with natural diversity and identifying hidden sources. [europepmc]
• Efficient and generalized processing of multidimensional NUS NMR data: the NESTA algorithm and comparison of regularization terms. [europepmc]
• Pitfalls in compressed sensing reconstruction and how to avoid them. [europepmc]
• Large Metasurface Aperture for Millimeter Wave Computational Imaging at the Human-Scale. [europepmc]
• Learning partial differential equations via data discovery and sparse optimization. [europepmc]
• Discovering sparse transcription factor codes for cell states and state transitions during development. [europepmc]
• A very large-scale microelectrode array for cellular-resolution electrophysiology. [europepmc]
• Deep-learning-based ghost imaging. [europepmc]
• Fast and accurate edge orientation processing during object manipulation. [europepmc]
• Robust data-driven discovery of governing physical laws with error bars. [europepmc]
• Front-end Weber-Fechner gain control enhances the fidelity of combinatorial odor coding. [europepmc]
• Learning to synthesize: robust phase retrieval at low photon counts. [europepmc]
• Broadband perovskite quantum dot spectrometer beyond human visual resolution. [europepmc]
• Endo-microscopy beyond the Abbe and Nyquist limits. [europepmc]
• Compressed sensing MRI: a review from signal processing perspective. [europepmc]
• Minutes-timescale 3D isotropic imaging of entire organs at subcellular resolution by content-aware compressed-sensing light-sheet microscopy. [europepmc]
• Compressed Sensing Real-Time Cine Reduces CMR Arrhythmia-Related Artifacts. [europepmc]
• Light-sheets and smart microscopy, an exciting future is dawning. [europepmc]

Related

• Stable Signal Recovery from Incomplete and Inaccurate Measurements
• Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit
• Data recovery from corrupted observations via l1 minimization
• Stable Recovery of Structured Signals From Corrupted Sub-Gaussian Measurements
• Analysis ℓ₁-recovery with frames and Gaussian measurements