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We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information.
The expression of a tensor or a polyadic as a sum of products
F. L. Hitchcock · 1927
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Multiple invariants and generalized rank of a p-way matrix or tensor
F. L. Hitchcock · 1927
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On the Shannon capacity of a graph
L. Lovász · 1979
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Schwartz spaces, nuclear spaces, and tensor products
Y.-C. Wong · 1979
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Distributive lattices, affine semigroup rings and algebras with straightening laws
T. Hibi · 1987
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Tensor rank is NP-complete
J. Håstad · 1990
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Tensor Norms and Operator Ideals
A. Defant and K. Floret · 1992
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Matrix Analysis
R. Bhatia · 1996
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Algebraic measures of entanglement
J.-L. Brylinski · 2002
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Matrix rank minimization with applications
M. Fazel · 2002
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Introduction to Tensor Products of Banach Spaces
R. A. Ryan · 2002
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Convex Optimization
S. Boyd and L. Vandenberghe · 2004
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Using algebraic geometry
D. Cox, J. Little, and D. O’Shea · 2005
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Bruno Buchberger’s PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
B. Buchberger · 2006
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
E. J. Candès, T. Tao, and J. K. Romberg · 2006
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Compressed sensing
D. L. Donoho · 2006
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Ideals, varieties, and algorithms
D. Cox, J. Little, and D. O’Shea · 2007
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Tensor rank and ill-posedness of the best low-rank approximation problem
V. De Silva and L.-H. Lim · 2008
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs
J. Gouveia, M. Laurent, P. A. Parrilo, and R. R. Thomas · 2009
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Tensor completion for estimating missing values in visual data
J. Liu, P. Musialski, P. Wonka, and J. Ye · 2009
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The power of matrix completion: near-optimal convex relaxation
E. J. Candès and T. Tao · 2010
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Theta bodies for polynomial ideals
J. Gouveia, P. A. Parrilo, and R. R. Thomas · 2010
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Hierarchical singular value decomposition of tensors
L. Grasedyck · 2010
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Quantum state tomography via compressed sensing
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert · 2010
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Moments, positive polynomials and their applications
J. Lasserre · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. Parrilo · 2010
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PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candès, T. Strohmer, and V. Voroninski · 2013
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Hierarchical tucker tensor optimization-applications to tensor completion
C. Da Silva and F. J. Herrmann · 2013
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A Mathematical Introduction to Compressive Sensing
S. Foucart and H. Rauhut · 2013
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Most tensor problems are NP-hard
C. J. Hillar and L.-H. Lim · 2013
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Proximal algorithms
N. Parikh and S. Boyd · 2013
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Tensor tensor recovery via iterative hard thresholding
H. Rauhut, R. Schneider, and Ž. Stojanac · 2013
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An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems
K. Toh and S. Yun · 2010
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Estimation of low-rank tensors via convex optimization
R. Tomioka, K. Hayashi, and H. Kashima · 2010
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A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
X. Y. Zhao, D. F. Sun, and K. C. Toh · 2010
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Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements
E. J. Candès and Y. Plan · 2011
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Kronecker compressive sensing
M. F. Duarte and R. G. Baraniuk · 2011
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Tensor completion and low-n-rank tensor recovery via convex optimization
S. Gandy, B. Recht, and I. Yamada · 2011
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Multilinear multitask learning
B. Romera-Paredes, H. Aung, N. Bianchi-Berthouze, and M. Pontil · 2013
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Low-rank tensor completion by riemannian optimization
D. Kressner, M. Steinlechner, and B. Vandereycken · 2014
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Low rank matrix recovery from rank one measurements
R. Kueng, H. Rauhut, and U. Terstiege · 2014
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Generalized higher-order orthogonal iteration for tensor decomposition and completion
Y. Liu, F. Shang, W. Fan, J. Cheng, and H. Cheng · 2014
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Completing any low-rank matrix, provably
Y. Chen, S. Bhojanapalli, S. Sanghavi, and R. Ward · 2015
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Provable models for robust low-rank tensor recovery
B. Huang, C. Mu, D. Goldfarb, and J. Wright · 2015
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Parallel algorithms for tensor completion in the CP format
L. Karlsson, D. Kressner, and A. Uschmajew · 2015
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Simultaneously structured models with application to sparse and low-rank matrices
S. Oymak, A. Jalali, M. Fazel, Y. C. Eldar, and B. Hassibi · 2015
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Tensor completion in hierarchical tensor representations
H. Rauhut, R. Schneider, and Ž. Stojanac · 2015
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SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
L. Q. Yang, D. F. Sun, and K. C. Toh · 2015
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Nuclear Norm of Higher-Order Tensors
S. Friedland and L.-H. Lim · 2016
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Theta rank, levelness, and matroid minors
F. Grande and R. Sanyal · 2016
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Low rank tensor recovery via iterative hard thresholding
H. Rauhut, R. Schneider, and Ž. Stojanac · 2016
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Low-rank Tensor Recovery
Ž. Stojanac · 2016
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On tensor completion via nuclear norm minimization
M. Yuan and C.-H. Zhang · 2016
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