A simple test to check the optimality of a sparse signal approximation
Signal Processing - Sparse approximations in signal and image processing
On the stability of the basis pursuit in the presence of noise
Signal Processing - Sparse approximations in signal and image processing
Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
Sparse representations are most likely to be the sparsest possible
EURASIP Journal on Applied Signal Processing
Gaussian averages of interpolated bodies and applications to approximate reconstruction
Journal of Approximation Theory
Compression of facial images using the K-SVD algorithm
Journal of Visual Communication and Image Representation
Finding effective points by surrogate models with overcomplete bases
Journal of Computational and Applied Mathematics
Algorithms for subset selection in linear regression
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Journal of Machine Learning Research
Sparse Coding Neural Gas for the Separation of Noisy Overcomplete Sources
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Foundations and Trends in Signal Processing
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model
International Journal of Computer Vision
Image Denoising Using Sparse Representations
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Approaching the Time Dependent Cocktail Party Problem with Online Sparse Coding Neural Gas
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
A Convex Approach to Low Rank Matrix Approximation with Missing Data
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Compressive data gathering for large-scale wireless sensor networks
Proceedings of the 15th annual international conference on Mobile computing and networking
A fast approach for overcomplete sparse decomposition based on smoothed l0 norm
IEEE Transactions on Signal Processing
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
A compressive sensing data acquisition and imaging method for stepped frequency GPRs
IEEE Transactions on Signal Processing
Image sequence denoising via sparse and redundant representations
IEEE Transactions on Image Processing
Sparse image reconstruction for molecular imaging
IEEE Transactions on Image Processing
A plurality of sparse representations is better than the sparsest one alone
IEEE Transactions on Information Theory
Comparing measures of sparsity
IEEE Transactions on Information Theory
Compressed and privacy-sensitive sparse regression
IEEE Transactions on Information Theory
Further results on stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
Multimodal Sparse Features for Object Detection
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
A compressed sensing approach for biological microscopic image processing
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Necessary and sufficient conditions for sparsity pattern recovery
IEEE Transactions on Information Theory
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
An iterative Bayesian algorithm for sparse component analysis in presence of noise
IEEE Transactions on Signal Processing
Sparse approximate solution of partial differential equations
Applied Numerical Mathematics
Aggregation by exponential weighting and sharp oracle inequalities
COLT'07 Proceedings of the 20th annual conference on Learning theory
On the total variation dictionary model
IEEE Transactions on Image Processing
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
Fast sparse representation based on smoothed lo norm
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Sparse component analysis in presence of noise using an iterative EM-MAP algorithm
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Minimax rates of convergence for high-dimensional regression under lq-ball sparsity
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Monotone operator splitting for optimization problems in sparse recovery
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Two dimensional compressive classifier for sparse images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
IEEE Transactions on Audio, Speech, and Language Processing
Bounds on the number of identifiable outliers in source localization by linear programming
IEEE Transactions on Signal Processing
Time-frequency energy distributions meet compressed sensing
IEEE Transactions on Signal Processing
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
Concave programming for minimizing the zero-norm over polyhedral sets
Computational Optimization and Applications
Information-theoretic limits on sparse signal recovery: dense versus sparse measurement matrices
IEEE Transactions on Information Theory
Stable recovery of sparse signals and an oracle inequality
IEEE Transactions on Information Theory
A distributed sensor fusion algorithm for the inversion of sparse fields
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Group testing strategies for recovery of sparse signals in noise
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Compressed sensing for digital holographic microscopy
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
ℓ1-Sparse reconstruction of sharp point set surfaces
ACM Transactions on Graphics (TOG)
New bounds for restricted isometry constants
IEEE Transactions on Information Theory
Decentralized sparse signal recovery for compressive sleeping wireless sensor networks
IEEE Transactions on Signal Processing
Direction-of-arrival estimation using a mixed l2,0norm approximation
IEEE Transactions on Signal Processing
Asymptotic analysis of robust LASSOs in the presence of noise with large variance
IEEE Transactions on Information Theory
Coherence-based performance guarantees for estimating a sparse vector under random noise
IEEE Transactions on Signal Processing
On the stable recovery of the sparsest overcomplete representations in presence of noise
IEEE Transactions on Signal Processing
An improved smoothed l0approximation algorithm for sparse representation
IEEE Transactions on Signal Processing
Efficient measurement generation and pervasive sparsity for compressive data gathering
IEEE Transactions on Wireless Communications
Large scale visual classification via learned dictionaries and sparse representation
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part I
Fast block-sparse decomposition based on SL0
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Two-dimensional random projection
Signal Processing
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
A generalized cauchy distribution framework for problems requiring robust behavior
EURASIP Journal on Advances in Signal Processing - Special issue on robust processing of nonstationary signals
SIAM Journal on Scientific Computing
Model-Based Multiple Rigid Object Detection and Registration in Unstructured Range Data
International Journal of Computer Vision
Direct data domain STAP using sparse representation of clutter spectrum
Signal Processing
Improved stability conditions of BOGA for noisy block-sparse signals
Signal Processing
Full length article: On performance of greedy algorithms
Journal of Approximation Theory
Compressive sensing of underground structures using GPR
Digital Signal Processing
A novel predual dictionary learning algorithm
Journal of Visual Communication and Image Representation
SIAM Journal on Optimization
Efficient minimization for dictionary based sparse representation and signal recovery
Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies
Error bounds for convex parameter estimation
Signal Processing
Phase transition in limiting distributions of coherence of high-dimensional random matrices
Journal of Multivariate Analysis
Journal of Approximation Theory
In-situ soil moisture sensing: measurement scheduling and estimation using compressive sensing
Proceedings of the 11th international conference on Information Processing in Sensor Networks
Robust Estimation for an Inverse Problem Arising in Multiview Geometry
Journal of Mathematical Imaging and Vision
Bioinspired sparse spectro-temporal representation of speech for robust classification
Computer Speech and Language
Sparse regression learning by aggregation and Langevin Monte-Carlo
Journal of Computer and System Sciences
Coherence Pattern-Guided Compressive Sensing with Unresolved Grids
SIAM Journal on Imaging Sciences
A multi-stage framework for Dantzig selector and LASSO
The Journal of Machine Learning Research
Function-valued mappings, total variation and compressed sensing for diffusion MRI
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part II
Journal of Approximation Theory
Sparse Doppler-only snapshot imaging for space debris
Signal Processing
Denoising for Multiple Image Copies through Joint Sparse Representation
Journal of Mathematical Imaging and Vision
The dictionary approach for spherical deconvolution
Journal of Multivariate Analysis
OMP or BP? a comparison study of image fusion based on joint sparse representation
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part V
Multi-resolutive sparse approximations of d-dimensional data
Computer Vision and Image Understanding
Nonnegative matrix factorization on orthogonal subspace with smoothed l0 norm constrained
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Direct feedback control design for nonlinear systems
Automatica (Journal of IFAC)
Manifold based sparse representation for facial understanding in natural images
Image and Vision Computing
Computer Methods and Programs in Biomedicine
Detection of sparse targets with structurally perturbed echo dictionaries
Digital Signal Processing
Embedding new observations via sparse-coding for non-linear manifold learning
Pattern Recognition
Sparse signal reconstruction using decomposition algorithm
Knowledge-Based Systems
Attribute-efficient evolvability of linear functions
Proceedings of the 5th conference on Innovations in theoretical computer science
Automated identification of thoracolumbar vertebrae using orthogonal matching pursuit
Machine Vision and Applications
Variable selection in high-dimension with random designs and orthogonal matching pursuit
The Journal of Machine Learning Research
Multi-stage multi-task feature learning
The Journal of Machine Learning Research
Improved sparse coding under the influence of perceptual attention
Neural Computation
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Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further that the overcomplete system is incoherent, it is shown that the optimally sparse approximation to the noisy data differs from the optimally sparse decomposition of the ideal noiseless signal by at most a constant multiple of the noise level. As this optimal-sparsity method requires heavy (combinatorial) computational effort, approximation algorithms are considered. It is shown that similar stability is also available using the basis and the matching pursuit algorithms. Furthermore, it is shown that these methods result in sparse approximation of the noisy data that contains only terms also appearing in the unique sparsest representation of the ideal noiseless sparse signal.