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
Extensions of compressed sensing
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
The pattern memory of gene-protein networks
AI Communications - Network Analysis in Natural Sciences and Engineering
On Phase Transitions in Learning Sparse Networks
ECML '07 Proceedings of the 18th European conference on Machine Learning
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Matching pursuit based on nonparametric waveform estimation
Digital Signal Processing
Further results on stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Restricted isometry constants where lpsparse recovery can fail for 0
IEEE Transactions on Information Theory
On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
The identification of dynamic gene-protein networks
KDECB'06 Proceedings of the 1st international conference on Knowledge discovery and emergent complexity in bioinformatics
Sparse gene regulatory network identification
KDECB'06 Proceedings of the 1st international conference on Knowledge discovery and emergent complexity in bioinformatics
Direction finding of multiple emitters by spatial sparsity and linear programming
ISCIT'09 Proceedings of the 9th international conference on Communications and information technologies
Bounds on the number of identifiable outliers in source localization by linear programming
IEEE Transactions on Signal Processing
Average case analysis of multichannel sparse recovery using convex relaxation
IEEE Transactions on Information Theory
Theoretical and empirical results for recovery from multiple measurements
IEEE Transactions on Information Theory
Stable recovery of sparse signals and an oracle inequality
IEEE Transactions on Information Theory
Dense error correction via l1-minimization
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Two conditions for equivalence of 0-norm solution and 1-norm solution in sparse representation
IEEE Transactions on Neural Networks
The generalized likelihood ratio test and the sparse representations approach
ICISP'10 Proceedings of the 4th international conference on Image and signal processing
Matrix sparsification and the sparse null space problem
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Sparse representations and approximation theory
Journal of Approximation Theory
Sparse Signal Reconstruction via Iterative Support Detection
SIAM Journal on Imaging Sciences
A coordinate gradient descent method for l1-regularized convex minimization
Computational Optimization and Applications
Error bounds for convex parameter estimation
Signal Processing
Recovery of sparse representations by polytope faces pursuit
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Phase transition in limiting distributions of coherence of high-dimensional random matrices
Journal of Multivariate Analysis
A Simpler Approach to Matrix Completion
The Journal of Machine Learning Research
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
Multi-resolutive sparse approximations of d-dimensional data
Computer Vision and Image Understanding
Mixed parametric/non-parametric identification of systems with discontinuous nonlinearities
Automatica (Journal of IFAC)
An Evaluation of the Sparsity Degree for Sparse Recovery with Deterministic Measurement Matrices
Journal of Mathematical Imaging and Vision
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The purpose of this contribution is to generalize some recent results on sparse representations of signals in redundant bases. The question that is considered is the following: given a matrix A of dimension (n,m) with mn and a vector b=Ax, find a sufficient condition for b to have a unique sparsest representation x as a linear combination of columns of A. Answers to this question are known when A is the concatenation of two unitary matrices and either an extensive combinatorial search is performed or a linear program is solved. We consider arbitrary A matrices and give a sufficient condition for the unique sparsest solution to be the unique solution to both a linear program or a parametrized quadratic program. The proof is elementary and the possibility of using a quadratic program opens perspectives to the case where b=Ax+e with e a vector of noise or modeling errors.