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In our recent work \cite{StojnicCSetam09,StojnicUpper10} we considered solving under-determined systems of linear equations with sparse solutions.
On the geometrical moments of skew regular simplices in hyperspherical space; with some applications in geometry and mathematical statistics
H. Ruben · 1960
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Non-linear angle-sum relations for polyhedral cones and polytopes
P. McMullen · 1975
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On Milman’s inequality and random subspaces which escape through a mesh in R n {R}^{n}
Y. Gordon · 1988
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Random projections of regular simplices
F. Afentranger and R. Schneider · 1992
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Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem
A. M. Vershik and P. V. Sporyshev · 1992
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Random projections of regular polytopes
K. Borocky and M. Henk · 1999
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Sparse representations in unions of bases
R. Gribonval and M. Nielsen · 2003
Earlier work this paper cites.
Neighborly polytopes and sparse solutions of underdetermined linear equations
D. Donoho · 2004
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On the strong uniqueness of highly sparse expansions from redundant dictionaries
R. Gribonval and M. Nielsen · 2004
Earlier work this paper cites.
Neighborliness of randomly-projected simplices in high dimensions
D. Donoho and J. Tanner · 2005
Earlier work this paper cites.
Sparse nonnegative solutions of underdetermined linear equations by linear programming
D. Donoho and J. Tanner · 2005
Cited alongside, same era.
Geometric approach to error correcting codes and reconstruction of signals
M. Rudelson and R. Vershynin · 2005
Cited alongside, same era.
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
E. Candes, J. Romberg, and T. Tao · 2006
Cited alongside, same era.
Combinatorial algorithms for compressed sensing
G. Cormode and S. Muthukrishnan · 2006
Cited alongside, same era.
High-dimensional centrally symmetric polytopes with neighborlines proportional to dimension
D. Donoho · 2006
Cited alongside, same era.
Algorithmic linear dimension reduction in the l1 norm for sparse vectors
A. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin · 2006
The restricted isometry property and its implications for compressed sensing
E. Candes · 2008
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Enhancing sparsity by reweighted l1 minimization
E. Candes, M. Wakin, and S. Boyd · 2008
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An alternating ell-1 approach to the compressed sensing problem
S. Chretien · 2008
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Stable sparse approximation via nonconvex optimization
R. Saab, R. Chartrand, and O. Yilmaz · 2008
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Thresholded basis pursuit: Quantizing linear programming solutions for optimal support recovery and approximation in compressed sensing
V. Saligrama and M. Zhao · 2008
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Cited alongside, same era.
One sketch for all: fast algorithms for compressed sensing
A. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin · 2007
Cited alongside, same era.
Highly sparse representations from dictionaries are unique and independent of the sparseness measure
R. Gribonval and M. Nielsen · 2007
Cited alongside, same era.
On sparse reconstruction from Fourier and Gaussian measurements
M. Rudelson and R. Vershynin · 2007
Cited alongside, same era.
A simple proof of the restricted isometry property for random matrices
R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin · 2008
Cited alongside, same era.
Restricted isometry constants where ell-p sparse recovery can fail for 0 < p ≤ 1 0<p\leq 1
M. E. Davies and R. Gribonval
Cited in the paper.
Sparsest solutions of underdetermined linear systems via ell-q minimization for 0 < q ≤ 1 0<q\leq 1
S. Foucart and M. J. Lai
Cited in the paper.
R. Adamczak, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann · 2009
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Block-length dependent thresholds in block-sparse compressed sensing
M. Stojnic · 2009
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A simple performance analysis of ℓ 1 \ell_{1} -optimization in compressed sensing
M. Stojnic · 2009
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Various thresholds for ℓ 1 \ell_{1} -optimization in compressed sensing
M. Stojnic · 2009
Later among the works it cites.