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We study the recovery of sparse vectors from subsampled random convolutions via $\ell_1$-minimization.
Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces
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Probability in Banach Spaces
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Atomic decomposition by basis pursuit
S. S. Chen, D. L. Donoho, and M. A. Saunders · 1998
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Decoupling. From Dependence to Independence
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5 n 5n Minkowski symmetrizations suffice to arrive at an approximate Euclidean ball
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Remarks on the geometry of coordinate projections in ℝ n \mathbb{R}^{n}
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
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Near optimal signal recovery from random projections: universal encoding strategies?
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Compressed sensing
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Random filters for compressive sampling and reconstruction
J. A. Tropp, M. B. Wakin, M. F. Duarte, D. Baron, and R. G. Baraniuk · 2006
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Toeplitz-structured compressed sensing matrices
W. U. Bajwa, J. D. Haupt, G. M. Raz, S. J. Wright, and R. D. Nowak · 2007
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Reconstruction and subgaussian operators in asymptotic geometric analysis
S. Mendelson, A. Pajor, and N. Tomczak Jaegermann · 2007
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A simple proof of the restricted isometry property for random matrices
R. G. Baraniuk, M. Davenport, R. A. DeVore, and M. Wakin · 2008
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On sparse reconstruction from Fourier and Gaussian measurements
M. Rudelson and R. Vershynin · 2008
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Fast dimension reduction using Rademacher series on dual BCH codes
N. Ailon and E. Liberty · 2009
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Counting faces of randomly-projected polytopes when the projection radically lowers dimension
D. L. Donoho and J. Tanner · 2009
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Uniform uncertainty principle for Bernoulli and subgaussian ensembles
S. Mendelson, A. Pajor, and N. Tomczak Jaegermann · 2009
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Circulant and Toeplitz matrices in compressed sensing
H. Rauhut · 2009
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Compressive sensing by random convolution
J. K. Romberg · 2009
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The Gelfand widths of ℓ p \ell_{p} -balls for 0 < p ≤ 1 0<p\leq 1
S. Foucart, A. Pajor, H. Rauhut, and T. Ullrich · 2010
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Toeplitz compressed sensing matrices with applications to sparse channel estimation
J. Haupt, W. U. Bajwa, G. Raz, and R. Nowak · 2010
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Fast and RIP-optimal transforms
N. Ailon and H. Rauhut · 2014
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An improved estimate in the restricted isometry problem
J. Bourgain · 2014
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Remote sensing via l1-minimization
M. Hügel, H. Rauhut, and T. Strohmer · 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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Upper and Lower Bounds For Stochastic Processes
M. Talagrand · 2014
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Nonuniform sparse recovery with random convolutions
D. James and H. Rauhut · 2015
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Compressive sensing and structured random matrices
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Sparsity in time-frequency representations
H. Rauhut and G. E. Pfander · 2010
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New and improved Johnson-Lindenstrauss embeddings via the restricted isometry property
F. Krahmer and R. Ward · 2011
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The convex geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P. Parrilo, and A. S. Willsky · 2012
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Restricted isometries for partial random circulant matrices
H. Rauhut, J. K. Romberg, and J. A. Tropp · 2012
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Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2012
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M. Kabanava and H. Rauhut · 2015
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Small ball probabilities for linear images of high-dimensional distributions
M. Rudelson and R. Vershynin · 2015
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On the gap between restricted isometry properties and sparse recovery conditions
S. Dirksen, G. Lecué, and H. Rauhut · 2016
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The restricted isometry property of subsampled Fourier matrices
I. Haviv and O. Regev · 2016
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Interpolation via weighted ℓ 1 \ell_{1} minimization
H. Rauhut and R. Ward · 2016
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One-bit compressed sensing with partial Gaussian circulant matrices
S. Dirksen, H. Jung, and H. Rauhut · 2017
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Refined analysis of sparse MIMO radar
D. Dorsch and H. Rauhut · 2017
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Sparse recovery under weak moment assumptions
G. Lecué and S. Mendelson · 2017
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