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In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$ (usually $m > n$, which is the overcomplete case).
Theory of Probability
S. Bernstein · 1927
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Probability inequalities for the sum of independent random variables
George Bennett · 1962
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Adaptive greedy approximations
Geoff Davis, Stephane Mallat, and Marco Avellaneda · 1997
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Sparse coding with an overcomplete basis set: A strategy employed by v1?
Bruno A Olshausen and David J Field · 1997
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Sanjoy Dasgupta · 1999
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Method of optimal directions for frame design
Kjersti Engan, Sven Ole Aase, and J Hakon Husoy · 1999
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Learning the parts of objects by non-negative matrix factorization
Daniel D Lee and H Sebastian Seung · 1999
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Learning overcomplete representations
Michael S Lewicki and Terrence J Sejnowski · 2000
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Uncertainty principles and ideal atomic decomposition
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Non-negative sparse coding
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K-svd and its non-negative variant for dictionary design
Michal Aharon, Michael Elad, and Alfred M Bruckstein · 2005
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Discriminative sparse image models for class-specific edge detection and image interpretation
Julien Mairal, Marius Leordeanu, Francis Bach, Martial Hebert, and Jean Ponce · 2008
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Image super-resolution as sparse representation of raw image patches
Jianchao Yang, John Wright, Thomas Huang, and Yi Ma · 2008
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Efficient and robust compressed sensing using optimized expander graphs
Sina Jafarpour, Weiyu Xu, Babak Hassibi, and A. Robert Calderbank · 2009
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Exact recovery of sparsely-used dictionaries
Daniel A. Spielman, Huan Wang, and John Wright · 2012
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Sparse feature learning for deep belief networks
Y-lan Boureau, Yann L Cun, et al · 2007
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New algorithms for learning incoherent and overcomplete dictionaries
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