The Geometry of Random {-1,1}-Polytopes
Discrete & Computational Geometry
On the stability of the basis pursuit in the presence of noise
Signal Processing - Sparse approximations in signal and image processing
Deterministic constructions of compressed sensing matrices
Journal of Complexity
The Gelfand widths of lp-balls for 0
Journal of Complexity
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
Dominating Subsets under Projections
SIAM Journal on Discrete Mathematics
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
On 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
Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization
SIAM Journal on Optimization
Advances in Computational Mathematics
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This paper is an attempt to both expound and expand upon, from an approximation theorist's point of view, some of the theoretical results that have been obtained in the sparse representation (compressed sensing) literature. In particular, we consider in detail @?"1^m-approximation, which is fundamental in the theory of sparse representations, and the connection between the theory of sparse representations and certain n-width concepts. We try to illustrate how the theory of sparse representation leads to new and interesting problems in approximation theory, while the results and techniques of approximation theory can further add to the theory of sparse representations.