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We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements.
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Tensor rank is NP-complete
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On global, local and stationary solutions in three-way data analysis
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Majorizing measures without measures
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Multilinear analysis of image ensembles: Tensorfaces
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Multidimensional filtering based on a tensor approach
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Out-of-core tensor approximation of multi-dimensional matrices of visual data
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
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Handwritten digit classification using higher order singular value decomposition
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From quantum to classical molecular dynamics: reduced models and numerical analysis
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Optimization algorithms on matrix manifolds
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Iterative hard thresholding for compressed sensing
T. Blumensath and M. Davies · 2009
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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. Thomas · 2009
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A new scheme for the tensor representation
W. Hackbusch and S. Kühn · 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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Breaking the curse of dimensionality, or how to use svd in many dimensions
I. V. Oseledets and E. E. Tyrtyshnikov · 2009
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Numerically exact quantum dynamics for indistinguishable particles: The multilayer multiconfiguration time-dependent hartree theory in second quantization representation
H. Wang and M. Thoss · 2009
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Normalized iterative hard thresholding: guaranteed stability and performance
T. Blumensath and M. Davies · 2010
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The power of convex relaxation: near-optimal matrix completion
E. J. Candès and T. Tao · 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, T. Flammia, S. Becker, and J. Eisert · 2010
Low-rank matrix completion by Riemannian optimization
B. Vandereycken · 2013
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An improved estimate in the restricted isometry problem
J. Bourgain · 2014
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Suprema of chaos processes and the restricted isometry property
F. Krahmer, S. Mendelson, and H. Rauhut · 2014
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Structured random measurements in signal processing
F. Krahmer and H. Rauhut · 2014
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Low-rank tensor completion by Riemannian optimization
D. Kressner, M. Steinlechner, and B. Vandereycken · 2014
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Square deal: Lower bounds and improved relaxations for tensor recovery
C. Mu, B. Huang, J. Wright, and D. Goldfarb · 2014
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Guaranteed rank minimization via singular value projection
P. Jain, R. Meka, and I. S. Dhillon · 2010
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Compressive sensing and structured random matrices
H. Rauhut · 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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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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Low-rank matrix recovery via iteratively reweighted least squares minimization
M. Fornasier, H. Rauhut, and R. Ward · 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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Tensorlab v2.0
L. Sorber, M. Van Barel, and L. De Lathauwer · 2014
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Upper and lower bounds for stochastic processes
M. Talagrand · 2014
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On tensor completion via nuclear norm minimization
M. Yuan and C.-H. Zhang · 2014
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Compressive multiplexing of correlated signals
A. Ahmed and J. Romberg · 2015
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Tensor prediction, Rademacher complexity and random 3-XOR
B. Barak and A. Moitra · 2015
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An iterative hard thresholding algorithm with improved convergence for low-rank tensor recovery
J. H. de Morais Goulart and G. Favier · 2015
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Tail bounds via generic chaining
S. Dirksen · 2015
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An Accelerated Iterative Hard Thresholding Method for Matrix Completion
J. Geng, X. Yang, X. Wang, and L. Wang · 2015
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Approximation algorithms for model-based compressive sensing
C. Hegde, P. Indyk, and L. Schmidt · 2015
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Stable low-rank matrix recovery via null space properties
M. Kabanava, R. Kueng, H. Rauhut, and U. Terstiege · 2015
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Isometric sketching of any set via restricted isometry property
S. Oymak, B. Recht, and M. Soltanolkotabi · 2015
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Tensor completion in hierarchical tensor representations
H. Rauhut, R. Schneider, and Ž. Stojanac · 2015
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Tensor theta norms and low rank recovery
H. Rauhut and Ž. Stojanac · 2015
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Optimal low-rank tensor recovery from separable measurements: Four contractions suffice
P. Shah, N. S. Rao, and G. Tang · 2015
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Riemannian optimization for high-dimensional tensor completion
M. Steinlechner · 2015
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The restricted isometry property of subsampled fourier matrices
I. Haviv and O. Regev · 2016
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