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Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework.
Convex analysis
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G. Watson · 1992
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Weak convergence
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Decoupling. From dependence to independence. Randomly stopped processes, U U -statistics and processes, martingales and beyond
V. de la Peña and E. Giné · 1998
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Convex optimization
S. Boyd and L. Vandenberghe · 2004
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Fast maximum margin matrix factorization for collaborative prediction
J. D. M. Rennie and N. Srebro · 2005
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Convex multi-task feature learning
A. Argyriou, T. Evgeniou, and M. Pontil · 2008
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Classical Fourier analysis. 2nd ed
L. Grafakos · 2008
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On sparse reconstruction from Fourier and Gaussian measurements
M. Rudelson and R. Vershynin · 2008
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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Compressed sensing and best k k -term approximation
A. Cohen, W. Dahmen, and R. DeVore · 2009
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Matrix completion with noise
E. J. Candès and Y. Plan · 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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Quantum state tomography via compressed sensing
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert · 2010
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Matrix completion from a few entries
R. H. Keshavan, A. Montanari, and S. Oh · 2010
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Matrix completion from noisy entries
R. H. Keshavan, A. Montanari, and S. Oh · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
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Stable principal component pursuit
Z. Zhou, X. Li, J. Wright, E. J. Candès, and Y. Ma · 2010
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Robust principal component analysis?
E. J. Candès, X. Li, Y. Ma, and J. Wright · 2011
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Constructing tight fusion frames
P. G. Casazza, M. Fickus, D. G. Mixon, Y. Wang, and Z. Zhou · 2011
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Optimally sparse frames
P. G. Casazza, A. Heinecke, F. Krahmer, and G. Kutyniok · 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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Recovering low-rank matrices from few coefficients in any basis
D. Gross · 2011
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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
V. Koltchinskii, K. Lounici, A. B. Tsybakov, et al · 2011
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Universal low-rank matrix recovery from pauli measurements
Y.-K. Liu · 2011
Cited alongside, same era.
A simpler approach to matrix completion
B. Recht · 2011
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The convex geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky · 2012
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Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
S. Negahban and M. J. Wainwright · 2012
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An introduction to matrix concentration inequalities
J. A. Tropp et al · 2015
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Matrix completion has no spurious local minimum
R. Ge, J. D. Lee, and T. Ma · 2016
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Stable low-rank matrix recovery via null space properties
M. Kabanava, R. Kueng, H. Rauhut, and U. Terstiege · 2016
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Low rank matrix recovery from clifford orbits
R. Kueng, H. Zhu, and D. Gross · 2016
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The generalized lasso with non-linear observations
Y. Plan and R. Vershynin · 2016
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Guaranteed matrix completion via non-convex factorization
R. Sun and Z.-Q. Luo · 2016
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Concentration inequalities: A nonasymptotic theory of independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candes, T. Strohmer, and V. Voroninski · 2013
Cited alongside, same era.
A mathematical introduction to compressive sensing
S. Foucart and H. Rauhut · 2013
Cited alongside, same era.
Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
Cited alongside, same era.
Probability in Banach Spaces: isoperimetry and processes
M. Ledoux and M. Talagrand · 2013
Cited alongside, same era.
Blind deconvolution using convex programming
A. Ahmed, B. Recht, and J. Romberg · 2014
Cited alongside, same era.
Optimal injectivity conditions for bilinear inverse problems with applications to identifiability of deconvolution problems
M. Kech and F. Krahmer · 2017
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Low rank matrix recovery from rank one measurements
R. Kueng, H. Rauhut, and U. Terstiege · 2017
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Sparse recovery under weak moment assumptions
G. Lecué and S. Mendelson · 2017
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Blind deconvolution meets blind demixing: Algorithms and performance bounds
S. Ling and T. Strohmer · 2017
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C. Ma, K. Wang, Y. Chi, and Y. Chen · 2017
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The leave-one-out approach for matrix completion: Primal and dual analysis
L. Ding and Y. Chen · 2018
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On the gap between restricted isometry properties and sparse recovery conditions
S. Dirksen, G. Lecué, and H. Rauhut · 2018
Later among the works it cites.
Blind deconvolution by a steepest descent algorithm on a quotient manifold
W. Huang and P. Hand · 2018
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Blind demixing and deconvolution at near-optimal rate
P. Jung, F. Krahmer, and D. Stöger · 2018
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Phase retrieval without small-ball probability assumptions
F. Krahmer and Y.-K. Liu · 2018
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Blind deconvolution: Convex geometry and noise robustness
F. Krahmer and D. Stöger · 2018
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Harmonic mean iteratively reweighted least squares for low-rank matrix recovery
C. Kümmerle and J. Sigl · 2018
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Rapid, robust, and reliable blind deconvolution via nonconvex optimization
X. Li, S. Ling, T. Strohmer, and K. Wei · 2018
Later among the works it cites.
Y. Chen, Y. Chi, J. Fan, C. Ma, and Y. Yan · 2019
Closest in time.
Low-rank matrix recovery via rank one tight frame measurements
H. Rauhut and U. Terstiege · 2019
Closest in time.