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In this paper we look at a connection between the $\ell_q,0\leq q\leq 1$, optimization and under-determined linear systems of 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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Some inequalities for gaussian processes and applications
Y. Gordon · 1985
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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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Uncertainty principles and ideal atomic decompositions
D. L. Donoho and X. Huo · 2001
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On sparse representation in pairs of bases
A. Feuer and A. Nemirovski · 2003
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Sparse representations in unions of bases
R. Gribonval and M. Nielsen · 2003
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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
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Greed is good: algorithmic results for sparse approximations
J. A. Tropp · 2004
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Neighborliness of randomly-projected simplices in high dimensions
D. Donoho and J. Tanner · 2005
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Sparse nonnegative solutions of underdetermined linear equations by linear programming
D. Donoho and J. Tanner · 2005
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Geometric approach to error correcting codes and reconstruction of signals
M. Rudelson and R. Vershynin · 2005
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
E. Candes, J. Romberg, and T. Tao · 2006
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Combinatorial algorithms for compressed sensing
G. Cormode and S. Muthukrishnan · 2006
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High-dimensional centrally symmetric polytopes with neighborlines proportional to dimension
D. Donoho · 2006
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Thresholds for the recovery of sparse solutions via l 1 l_{1} minimization
D. Donoho and J. Tanner · 2006
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Compressed sensing
D. L. 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
Cited alongside, same era.
An alternating ell-1 approach to the compressed sensing problem
S. Chretien · 2008
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Subspace pursuit for compressive sensing signal reconstruction
W. Dai and O. Milenkovic · 2008
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Counting the face of randomly projected hypercubes and orthants with application
D. Donoho and J. Tanner · 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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Compressed sensing over the grassmann manifold: A unified analytical framework
W. Xu and B. Hassibi · 2008
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How neighborly can a centrally symmetric polytope be?
N. Linial and I. Novik · 2006
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Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit
D. L. Donoho, Y. Tsaig, I. Drori, and J.L. Starck · 2007
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.
Signal recovery from random measurements via orthogonal matching pursuit
J. Tropp and A. Gilbert · 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.
R. Adamczak, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann · 2009
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Message-passing algorithms for compressed sensing
D. Donoho, A. Maleki, and A. Montanari · 2009
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Counting faces of randomly projected polytopes when the projection radically lowers dimension
D. Donoho and J. Tanner · 2009
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CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
D. Needell and J. A. Tropp · 2009
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Unifrom uncertainly principles and signal recovery via regularized orthogonal matching pursuit
D. Needell and R. Vershynin · 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
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On the reconstruction of block-sparse signals with an optimal number of measurements
M. Stojnic, F. Parvaresh, and B. Hassibi · 2009
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Towards improving ℓ 1 \ell_{1} optimization in compressed sensing
M. Stojnic · 2010
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