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In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal.
Spin-Glass Theory and Beyond
M. Mézard, G. Parisi, and M. A. Virasoro, · 1987
Earlier work this paper cites.
“Sparse nonnegative solution of underdetermined linear equations by linear programming,”
David L. Donoho and Jared Tanner, · 2005
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“Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?,”
E. J. Candès and T. Tao, · 2006
Earlier work this paper cites.
“Compressed sensing,”
D. L. Donoho, · 2006
Earlier work this paper cites.
Modern Coding Theory
Tom Richardson and Rüdiger Urbanke, · 2008
Earlier work this paper cites.
“Message-passing algorithms for compressed sensing,”
David L. Donoho, Arian Maleki, and Andrea Montanari, · 2009
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S. Rangan, A.K. Fletcher, and V. Goyal, · 2009
Earlier work this paper cites.
“A single-letter characterization of optimal noisy compressed sensing,”
Dongning Guo, D. Baron, and S. Shamai, · 2009
Cited alongside, same era.
“A typical reconstruction limit of compressed sensing based on lp-norm minimization,”
Y. Kabashima, T. Wadayama, and T. Tanaka, · 2009
Cited alongside, same era.
“Sparse recovery under matrix uncertainty,”
M. Rosenbaum and A. Tsybakov, · 2010
Cited alongside, same era.
“Message passing algorithms for compressed sensing: I. motivation and construction,”
D.L. Donoho, A. Maleki, and A. Montanari, · 2010
Cited alongside, same era.
“Sparsity-cognizant total leastsquares for perturbed compressive sampling,”
H. Zhu, G. Leus, and G. Giannakis, · 2011
Cited alongside, same era.
“Compressive sensing under matrix uncertainties: An approximate message passing approach,”
J.T. Parker, V. Cevher, and P. Schniter, · 2011
“Expectation-maximization bernoulli-gaussian approximate message passing,”
J. P. Vila and P. Schniter, · 2011
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“The dynamics of message passing on dense graphs, with applications to compressed sensing,”
M. Bayati and A. Montanari, · 2011
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“Statistical physics-based reconstruction in compressed sensing,”
F. Krzakala, M. Mézard, F. Sausset, Y.F. Sun, and L. Zdeborová, · 2012
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“Probabilistic reconstruction in compressed sensing: Algorithms, phase diagrams, and threshold achieving matrices,”
F. Krzakala, M. Mézard, F. Sausset, Y.F. Sun, and L. Zdeborová, · 2012
Later among the works it cites.
“Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,”
David L. Donoho, Adel Javanmard, and Andrea Montanari, · 2012
Later among the works it cites.
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Cited alongside, same era.
“Generalized approximate message passing for estimation with random linear mixing,”
S. Rangan, · 2011
Cited alongside, same era.
“Compressed sensing of approximately-sparse signals: Phase transitions and optimal reconstruction,”
J. Barbier, F. Krzakala, M. Mézard, and L. Zdeborová, · 2012
Later among the works it cites.