Eigenvalues and condition numbers of random matrices
SIAM Journal on Matrix Analysis and Applications
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Greedy algorithms and M-term approximation with regard to redundant dictionaries
Journal of Approximation Theory
On the Optimality of the Backward Greedy Algorithm for the Subset Selection Problem
SIAM Journal on Matrix Analysis and Applications
Atomic Decomposition by Basis Pursuit
SIAM Review
Approximation of functions over redundant dictionaries using coherence
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Foundations of Computational Mathematics
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
A generalized uncertainty principle and sparse representation in pairs of bases
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Designing structured tight frames via an alternating projection method
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
The curvelet transform for image denoising
IEEE Transactions on Image Processing
On Sparsity Maximization in Tomographic Particle Image Reconstruction
Proceedings of the 30th DAGM symposium on Pattern Recognition
Comparing measures of sparsity
IEEE Transactions on Information Theory
Embedding new observations via sparse-coding for non-linear manifold learning
Pattern Recognition
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Given a signal S ∈ RN and a full-rank matrix D ∈ RN×L with N , we define the signal's overcomplete representations as all α ∈ RL satisfying S = Dα. Among all the possible solutions, we have special interest in the sparsest one--the one minimizing ||α||o. Previous work has established that a representation is unique if it is sparse enough, requiring ||α||o o