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This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements.
Regression shrinkage and selection via the LASSO
R. Tibshirani · 1996
Earlier work this paper cites.
Atomic decomposition by basis pursuit
S. S. Chen, D. L. Donoho, and M. A. Saunders · 1998
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Asymptotics for LASSO-type estimators
K. Knight and W. Fu · 2000
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Function estimation and gaussian sequence model
I. M. Johnstone · 2002
Earlier work this paper cites.
Convex optimization
S. Boyd and L. Vanderberghe · 2004
Earlier work this paper cites.
Least angle regression
B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani · 2004
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Neighborliness of randomly projected simplices in high dimensions
D. L. Donoho and J. Tanner · 2005
Earlier work this paper cites.
Stable recovery of sparse overcomplete representations in the presence of noise
D. L. Donoho, M. Elad, and V. Temlyakov · 2006
Earlier work this paper cites.
Just relax: Convex programming methods for identifying sparse signals
J. A. Tropp · 2006
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On model selection consistency of LASSO
P. Zhao and B. Yu · 2006
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High-dimensional graphs and variable selection with the LASSO
N. Meinshausen and P. Bühlmann · 2006
Earlier work this paper cites.
High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
D. L. Donoho · 2006
Earlier work this paper cites.
Sparsity oracle inequalities for the LASSO
F. Bunea, A. Tsybakov, and M. Wegkamp · 2007
Cited alongside, same era.
On the degrees of freedom of the LASSO
H. Zou, T. Hastie, and R. Tibshirani · 2007
Cited alongside, same era.
LASSO-type recovery of sparse representations for high-dimensional data
N. Meinshausen and B. Yu · 2009
Cited alongside, same era.
Simultaneous analysis of LASSO and Dantzig selector
P. Bickel, Y. Ritov, and A. Tsybakov · 2009
Cited alongside, same era.
On the conditions used to prove oracle results for the LASSO
S. van de Geer and P. Bühlmann · 2009
Cited alongside, same era.
Counting faces of randomly projected polytopes when the projection radically lowers dimension
D. L. Donoho and J. Tanner · 2009
Various thresholds for ℓ _ 1 \ell\_1 -optimization in compressed sensing
M. Stojnic · 2009
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Precise undersampling theorems
D. L. Donoho and J. Tanner · 2010
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Approximate message passing algorithm for compressed sensing
A. Maleki · 2010
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Coherence analysis of iterative thresholding algorithms
A. Maleki · 2010
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Analysis of approximate message passing algorithm
A. Maleki and A. Montanari · 2010
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The dynamics of message passing on dense graphs, with applications to compressed sensing
M. Bayati and A. Montanri · 2011
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Cited alongside, same era.
Observed universality of phase transitions in high-dimensional geometry, with applications in modern signal processing and data analysis
D. L. Donoho and J. Tanner · 2009
Cited alongside, same era.
Message passing algorithms for compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2009
Cited alongside, same era.
Iterative hard thresholding for compressed sensing
T. Blumensath and M. E. Davies · 2009
Cited alongside, same era.
How to use the iterative hard thresholding algorithm
T. Blumensath and M. E. Davies · 2009
Cited alongside, same era.
Application of compressive sensing to the design of wideband signal acquisition receivers
J. Treichler, M. A. Davenport, and R. G. Baraniuk · 2009
Cited alongside, same era.
The LASSO risk for Gaussian matrices
M. Bayati and A. Montanari
Cited in the paper.
Noise sensitivity phase transition
D. L. Donoho, A. Maleki, and A. Montanari · 2011
Later among the works it cites.
On a relation between the minimax risk and the phase transitions of compressed recovery
S. Oymak and B. Hassibi · 2012
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Universality in polytope phase transitions and message passing algorithms
M. Bayati, M. Lelarge, and A. Montanari · 2012
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The pros and cons of compressive sensing for wideband signal acquisition: Noise folding versus dynamic range
M. A. Davenport, J. N Laska, J. R Treichler, and R. G. Baraniuk · 2012
Later among the works it cites.
Living on the edge: A geometric theory of phase transitions in convex optimization
D. Amelunxen, M. Lotz, M. B. McCoy, and J. A. Tropp · 2013
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