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Recently, \cite{CRT,DonohoPol} theoretically analyzed the success of a polynomial $\ell_1$-optimization algorithm in solving an under-determined system of linear equations.
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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The asymptotic distribution of the trimmed mean
S. M. Stigler · 1973
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Non-linear angle-sum relations for polyhedral cones and polytopes
P. McMullen · 1975
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Norms of gaussian sample functions
B. S. Cirelson, I. A. Ibragimov, and V. N. Sudakov · 1976
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Probabilistic methods in the geometry of banach spaces
G. Pisier · 1986
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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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Uncertainty principles and ideal atomic decompositions
D. L. Donoho and X. Huo · 2001
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Sparse channel estimation via matching pursuit with application to equalization
S. F. Cotter and B. D. Rao · 2002
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Convex Optimization
S. Boyd and L. Vandenberghe · 2003
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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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A remark on simultaneous greedy approximation
V.N. Temlyakov · 2004
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Greed is good: algorithmic results for sparse approximations
J. A. Tropp · 2004
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Distributed compressed sensing
D. Baron, M. Wakin, M. Duarte, S. Sarvotham, and Richard Baraniuk · 2005
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Decoding by linear programming
E. Candes and T. Tao · 2005
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Sparse solutions to linear inverse problems with multiple measurement vectors
S. Cotter, B. Rao, K. Engan, and K. Kreutz-Delgado · 2005
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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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Sampling and reconstruction of signals with finite rate of innovation in the presence of noise
I. Maravic and M. Vetterli · 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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Algorithms for simultaneous sparse approximation. part i: Greedy pursuit
J. Tropp, A. C. Gilbert, and M. Strauss · 2005
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Approximating orthogonal matrices by permutation matrices
A. Barvinok · 2006
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Compressive sampling
E. Candes · 2006
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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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Theoretical results on sparse representations of multiple-measurement vectors
J. Chen and X. Huo · 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
Cited alongside, same era.
Thresholds for the recovery of sparse solutions via l 1 l_{1} minimization
D. Donoho and J. Tanner · 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.
Signal reconstruction from noisy random projections
J. Haupt and R. Nowak · 2006
Cited alongside, same era.
How neighborly can a centrally symmetric polytope be?
N. Linial and I. Novik · 2006
Cited alongside, same era.
Sharp thresholds for high-dimensional and noisy recovery of sparsity
M. J. Wainwright · 2006
Cited alongside, same era.
Recovering sparse signals using sparse measurement matrices in compressed dna microarrays
F. Parvaresh, H. Vikalo, S. Misra, and B. Hassibi · 2008
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Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization
B. Recht, W. Xu, and B. Hassibi · 2008
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Sparse representations for image classification: Learning discriminative and reconstructive non-parametric dictionaries
F. Rodriguez and G. Sapiro · 2008
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Imaging via compressive sampling
J. Romberg · 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
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Random weighting, asymptotic counting, and inverse isoperimetry
A. Barvinok and A. Samorodnitsky · 2007
Cited alongside, same era.
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.
The price of privacy and the limits of lp decoding
C. Dwork, F. McSherry, and K. Talwar · 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.
Compressed sensing meets bionformatics: a new DNA microarray architecture
O. Milenkovic, R. Baraniuk, and T. Simunic-Rosing · 2007
Cited alongside, same era.
V. Saligrama and M. Zhao · 2008
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Compressed sensing of approximately sparse signals
M. Stojnic, W. Xu, and B. Hassibi · 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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Sparsity-enforced slice-selective mri rf excitation pulse design
A. C. Zelinski, L. L. Wald, K. Setsompop, V. K. Goyal, and E. Adalsteinsson · 2008
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R. Adamczak, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann · 2009
Closest in time.
Sampling theorems for signals from the union of finite-dimensional linear subspaces
T. Blumensath and M. E. Davies · 2009
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Recovery of clustered sparse signals from compressive measurements
V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk · 2009
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Compressed sensing and best k-term approximation
A. Cohen, W. Dahmen, and R. DeVore · 2009
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D. Donoho and J. Tanner · 2009
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Block-sparsity: Coherence and efficient recovery
Y. C. Eldar and H. Bolcskei · 2009
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Compressed sensing of block-sparse signals: Uncertainty relations and efficient recovery
Y. C. Eldar, P. Kuppinger, and H. Bolcskei · 2009
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Separation of a subspace-sparse signal: Algorithms and conditions
A. Ganesh, Z. Zhou, and Y. Ma · 2009
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Sparse recovery of positive signals with minimal expansion
M. A. Khajehnejad, A. G. Dimakis, W. Xu, and B. Hassibi · 2009
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Weighted ℓ 1 \ell_{1} minimization for sparse recovery with prior information
M. A. Khajehnejad, W. Xu, S. Avestimehr, and B. Hassibi · 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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S. Negahban and M. J. Wainwright · 2009
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ℓ 2 / ℓ 1 \ell_{2}/\ell_{1} -optimization in block-sparse compressed sensing and its strong thresholds
M. Stojnic · 2009
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Explicit thresholds for approximately sparse compressed sensing via ℓ 1 \ell_{1} -optimization
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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Strong thresholds for ℓ 2 / ℓ 1 \ell_{2}/\ell_{1} -optimization in block-sparse 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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W. Xu, M. A. Khajehnejad, S. Avestimehr, and B. Hassibi · 2009
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Joint-sparse recovery from multiple measurements
E. van den Berg and M. P. Friedlander · 2051
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A. C. Zelinski, V. K. Goyal, and E. Adalsteinsson · 2083
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