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We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse.
‘Wald’s lemma’ for sums of order statistics of i.i.d. random variables
F. Thomas Bruss and James B. Robertson · 1991
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Statistics of natural images: Scaling in the woods
D.L. Ruderman and W. Bialek · 1994
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1994
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Atomic decomposition by basis pursuit
S. Chen, D.L. Donoho, and M.A. Saunders · 1999
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Wavelet statistical models and besov spaces
H. Choi and R.G. Baraniuk · 1999
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Adaptive wavelet thresholding for image denoising and compression
G. Chang, B. Yu, and M. Vetterli · 2000
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Compressive sensing over the grassmann manifold: a unified geometric framework
W. Xu and B. . Hassibi · 2000
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A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics
D. Martin, C. Fowlkes, D. Tal, and J. Malik · 2001
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Natural image statistics and neural representation
E.P. Simoncelli and B.A. Olshausen · 2001
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Image denoising using scale mixtures of gaussians in the wavelet domain
J. Portilla, V. Strela, M.J. Wainwright, and E.P. Simoncelli · 2003
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Near-optimal signal recovery from random projections: universal encoding strategies?
E. J. Candès and Terence Tao · 2004
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On the strong uniqueness of highly sparse expansions from redundant dictionaries
Rémi Gribonval and Morten Nielsen · 2004
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Math 710: Measure concentration
Alexander Barvinok · 2005
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Stable signal recovery from incomplete and inaccurate measurements
E. J. Candès, J. Romberg, and Terence Tao · 2006
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Compressed sensing
David L. Donoho · 2006
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A simple test to check the optimality of sparse signal approximations
Rémi Gribonval, Rosa Maria Figueras i Ventura, and Pierre Vandergheynst · 2006
Cited alongside, same era.
Highly sparse representations from dictionaries are unique and independent of the sparseness measure
Rémi Gribonval and Morten Nielsen · 2007
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A new view of automatic relevance determination
David Wipf and Srikantan Nagarajan · 2008
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Sampling theorems for signals from the union of finite-dimensional linear subspaces
Thomas Blumensath and Michael E. Davies · 2009
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Compressed sensing and best k-term approximation
Albert Cohen, Wolfgang Dahmen, and Ronald A. DeVore · 2009
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On lp minimisation, instance optimality, and restricted isometry constants for sparse approximation
M. E. Davies and Rémi Gribonval · 2009
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Instance-optimality in probability with an l1-minimization decoder
Ronald DeVore, Guergana Petrova, and Przemyslaw Wojtaszczyk · 2009
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Counting faces of randomly-projected polytopes when the projection radically lowers dimension
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Model distortions in Bayesian MAP reconstruction
Mila Nikolova · 2007
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The restricted isometry property and its implications for compressed sensing
Emmanuel Candès · 2008
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Learning with compressible priors
V. Cevher · 2008
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Aspects of Multivariate Statistical Theory
Robb J. Muirhead · 2008
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Compressed sensing and bayesian experimental design
M. Seeger and H. Nickisch · 2008
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David Donoho and Jared Tanner · 2009
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Probability, Random Processes, and Ergodic Properties
Robert M. Gray · 2009
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Low-dimensional models for dimensionality reduction and signal recovery: A geometric perspective
R.G. Baraniuk, V. Cevher, and M.B. Wakin · 2010
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Compressibility of deterministic and random infinite sequences
Arash Amini, Michael Unser, and Farokh Marvasti · 2011
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Compressed sensing over ℓ p \ell_{p} -balls: Minimax mean square error
David L. Donoho, Iain Johnstone, Arian Maleki, and Andrea Montanari · 2011
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Should penalized least squares regression be interpreted as Maximum A Posteriori estimation?
Rémi Gribonval · 2011
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