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This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals.
Introductory functional analysis with applications , volume 1
E. Kreyszig · 1978
Earlier work this paper cites.
On the L4 norm of spherical harmonics
R. J. Stanton and A. Weinstein · 1981
Earlier work this paper cites.
A note on a theorem of Stanton-Weinstein on the L4-norm of spherical harmonics
J.-H. Lu · 1987
Earlier work this paper cites.
Some np-complete problems in quadratic and nonlinear programming
K. G. Murty and S. N. Kabadi · 1987
Earlier work this paper cites.
Jacobi’s method is more accurate than qr
J. Demmel and K. Veselić · 1992
Earlier work this paper cites.
New perturbation bounds for the unitary polar factor
R.-C. Li · 1995
Earlier work this paper cites.
Sparse approximate solutions to linear systems
B. K. Natarajan · 1995
Earlier work this paper cites.
Wavelets and subband coding
M. Vetterli and J. Kovacevic · 1995
Earlier work this paper cites.
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
B. A. Olshausen and D. J. Field · 1996
Earlier work this paper cites.
Nonlinear programming
D. P. Bertsekas · 1997
Earlier work this paper cites.
A family of fixed-point algorithms for independent component analysis
A. Hyvärinen · 1997
Earlier work this paper cites.
A fast fixed-point algorithm for independent component analysis
A. Hyvärinen and E. Oja · 1997
Earlier work this paper cites.
Sparse coding with an overcomplete basis set: A strategy employed by v1?
B. A. Olshausen and D. J. Field · 1997
Earlier work this paper cites.
The geometry of algorithms with orthogonality constraints
A. Edelman, T. A. Arias, and S. T. Smith · 1998
Earlier work this paper cites.
Gradient-based learning applied to document recognition
Y. LeCun, L. Bottou, Y. Bengio, P. Haffner, et al · 1998
Earlier work this paper cites.
Discrete-time signal processing
A. V. Oppenheim · 1999
Earlier work this paper cites.
An introduction to harmonic analysis
Y. Katznelson · 2004
Earlier work this paper cites.
Decoding by linear programming
E. Candes and T. Tao · 2005
Earlier work this paper cites.
K-svd: An algorithm for designing overcomplete dictionaries for sparse representation
M. Aharon, M. Elad, A. Bruckstein, et al · 2006
Earlier work this paper cites.
For most large underdetermined systems of linear equations the minimal ℓ 1 \ell^{1} -norm solution is also the sparsest solution
D. L. Donoho · 2006
Earlier work this paper cites.
Image denoising via sparse and redundant representations over learned dictionaries
M. Elad and M. Aharon · 2006
Earlier work this paper cites.
Sparse feature learning for deep belief networks
M. Ranzato, Y. Boureau, and Y. LeCun · 2007
Earlier work this paper cites.
Convex multi-task feature learning
A. Argyriou, T. Evgeniou, and M. Pontil · 2008
Earlier work this paper cites.
Discriminative learned dictionaries for local image analysis
J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman · 2008
Earlier work this paper cites.
Optimization algorithms on matrix manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2009
Cited alongside, same era.
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J. Mairal, J. Ponce, G. Sapiro, A. Zisserman, and F. R. Bach · 2009
Cited alongside, same era.
Proximal methods for sparse hierarchical dictionary learning
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Cited alongside, same era.
Generalized power method for sparse principal component analysis
M. Journée, Y. Nesterov, P. Richtárik, and R. Sepulchre · 2010
Cited alongside, same era.
Best basis compressed sensing
G. Peyre · 2010
Cited alongside, same era.
Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
Cited alongside, same era.
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Later among the works it cites.
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S. Ravishankar and Y. Bresler · 2015
Later among the works it cites.
Complete dictionary recovery over the sphere
J. Sun, Q. Qu, and J. Wright · 2015
Later among the works it cites.
S. Wu and B. Yu · 2015
Later among the works it cites.
Polynomial-time tensor decompositions with sum-of-squares
T. Ma, J. Shi, and D. Steurer · 2016
Later among the works it cites.
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J. Mairal, F. Bach, and J. Ponce · 2012
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Subgradient descent learns orthogonal dictionaries
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Nonconvex optimization meets low-rank matrix factorization: An overview
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Stochastic subgradient method converges on tame functions
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