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We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix.
On a lemma of Littlewood and Offord
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Independent component analysis: A new concept?
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Emergence of simple-cell receptive field properties by learning a sparse code for natural images
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Method of optimal directions for frame design
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Blind source separation by sparse decomposition
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Dictionary learning algorithms for sparse representation
K. Kreutz-Delgado, J. Murray, B. Rao, K. Engan, T. Lee, and T. Sejnowski · 2003
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Blind source separation with relative newton method
M. Zibulevsky · 2003
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Sparse component analysis and blind source separation of underdetermined mixtures
P. Georgiev, F. Theis, and A. Cichocki · 2005
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The K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation
M. Aharon, M. Elad, and A. Bruckstein · 2006
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On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them
M. Elad M. Aharon and A. Bruckstein · 2006
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Dictionary learning for ℓ 1 \ell^{1} -exact sparse coding
M. Plumbley · 2007
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Convex sparse matrix factorizations
F. Bach, J. Mairal, and J. Ponce · 2008
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Matrix sparsification and the sparse null space problem
L-A. Gottlieb and T. Neylon · 2010
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Dictionary identification-sparse matrix-factorisation via l 1 l_{1} -minimisation
R. Gribonval and K. Schnass · 2010
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An l1 criterion for dictionary learning by subspace identification
F. Jaillet, R. Gribonval, M. Plumbley, and H. Zayyani · 2010
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Dictionaries for sparse representation modeling
R. Rubinstein, A. Bruckstein, and M. Elad · 2010
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Image super-resolution via sparse representation
J. Yang, J. Wright, T. Huang, and Y. Ma · 2010
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On the local correctness of ℓ 1 \ell^{1} minimization for dictionary learning
Q. Geng and J. Wright · 2011
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From sparse solutions of systems of equations to sparse modeling of signals and images
A. M. Bruckstein, D. L. Donoho, and M. Elad · 2009
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Online dictionary learning for sparse coding
J. Mairal, F. Bach, J. Ponce, and G. Sapiro · 2009
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On variants of the johnson-lindenstrauss lemma
Jiri Matousek
Cited in the paper.
The sample complexity of dictionary learning
D. Vainsencher, S. Mannor, and A. Bruckstein · 2011
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