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This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation.
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Blind source separation by sparse decomposition in a signal dictionary
M. Zibulevsky and B. A. Pearlmutter · 2001
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Optimally sparse representation in general (non-orthogonal) dictionaries via ℓ 1 \ell_{1} minimization
D. Donoho and M. Elad · 2003
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Sparse representations in unions of bases
R. Gribonval and M. Nielsen · 2003
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Dictionary learning algorithms for sparse representation
K. Kreutz-Delgado, J.F. Murray, B.D. Rao, K. Engan, T. Lee, and Sejnowski T.J · 2003
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Greed is good: Algorithmic results for sparse approximation
J. Tropp · 2004
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Stable signal recovery from incomplete and inaccurate measurements
E. Candès, J. Romberg, and T. Tao · 2005
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On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them
M. Aharon, M. Elad, and A.M. Bruckstein · 2006
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Motif: An efficient algorithm for learning translation invariant dictionaries
P. Jost, S. Lesage, P. Vandergheynst, and R. Gribonval · 2006
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Linear program differentiation for single-channel speech separation
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Just relax: Convex programming methods for subset selection and sparse approximation
J. Tropp · 2006
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Dictionary learning for ℓ 1 \ell_{1} -exact sparse coding
M.D. Plumbley · 2007
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Uniform uncertainty principle for Bernoulli and subgaussian ensembles
S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann · 2008
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Sparse component analysis and blind source separation of underdetermined mixtures
P. Georgiev, F. J. Theis, and A. Cichocki · 2005
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Geometry and homotopy for ℓ 1 \ell^{1} sparse signal representations
M. Plumbley · 2005
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K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation
M. Aharon, M. Elad, and A. M. Bruckstein · 2006
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G. Tauböck, D. Eiwen, F. Hlawatsch and H. Rauhut, Compressive estimation of doubly selective channels: exploiting channel sparsity to improve spectral efficiency in multicarrier transmissions, IEEE Journal of Selected Topics in Signal Processing
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Identification of matrices having a sparse representation
G. Pfander, H. Rauhut, and J. Tanner · 2008
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On the conditioning of random subdictionaries
J.A. Tropp · 2008
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Regularized dictionary learning for sparse approximation
M. Yaghoobi, T. Blumensath, and M.E. Davies · 2008
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