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Duke Mathematical Journal, ISSN 0012-7094, 07/2011, Volume 159, Issue 1, pp. 145 - 185
We give a new explicit construction of n x N matrices satisfying the Restricted Isometry Property (RIP). Namely, for some epsilon > 0, large N, and any n... 
MATHEMATICS | RESTRICTED ISOMETRY PROPERTY | RECONSTRUCTION | SIGNAL RECOVERY | FOURIER | SUMS | 41A46 | 94B60 | 94A12 | 11B13 | 11B30 | 11T23
Journal Article
Constructive Approximation, ISSN 0176-4276, 12/2008, Volume 28, Issue 3, pp. 253 - 263
We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed... 
15A52 | Random matrices | 60F10 | Analysis | Numerical Analysis | Mathematics | Sampling | 94A12 | Compressed sensing | Concentration inequalities | 15N2 | 94A20 | MATHEMATICS | Computer science | Electrical engineering
Journal Article
International Journal of Control, ISSN 0020-7179, 04/2011, Volume 84, Issue 4, pp. 693 - 701
The tracking differentiator was first proposed by Han in 1989 and the proof of convergence was presented the first time in Han and Wang (Han, J.Q., and Wang,... 
tracking differentiator | 34K35 | 94A12 | 34D20 | 93C15 | stability | AUTOMATION & CONTROL SYSTEMS | FREQUENCY
Journal Article
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2013, Volume 19, Issue 6, pp. 1229 - 1254
Journal Article
Constructive Approximation, ISSN 0176-4276, 2/2017, Volume 45, Issue 1, pp. 113 - 127
This paper is concerned with the performance of orthogonal matching pursuit (OMP) algorithms applied to a dictionary $$\mathcal{D}$$ D in a Hilbert space... 
Orthogonal matching pursuit | 94A15 | 15A52 | 41A46 | Restricted isometry property | Numerical Analysis | Analysis | 68P30 | Mathematics | Instance optimality | 94A12 | Best n -term approximation | Best n-term approximation | MATHEMATICS | RECOVERY | SPARSE APPROXIMATION | Algorithms
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2009, Volume 3, pp. 1360 - 1392
Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the... 
Sparsity | Irrepresentable condition | Lasso | Coherence | Restricted isometry | Compatibility | Restricted eigenvalue | RECOVERY | DANTZIG SELECTOR | restricted isometry | MODEL SELECTION | STATISTICS & PROBABILITY | sparsity | compatibility | irrepresentable condition | restricted eigenvalue
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 04/2019, Volume 40, Issue 6, pp. 670 - 684
In this article, we mainly study the multivariate dynamical sampling in and shift-invariant spaces. We first provide a sufficient and necessary condition for... 
Dynamical sampling | 41A58 | multivariate dynamical sampling | 94A12 | 42C15 | shift-invariant spaces | 94A20 | MATHEMATICS, APPLIED | RECONSTRUCTION | THEOREMS | SIGNALS | SUBSPACES | Sampling | Invariants
Journal Article
JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 08/2019, Volume 80, Issue 2, pp. 762 - 783
In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an... 
MATHEMATICS, APPLIED | 62J05 | 65F22 | RECONSTRUCTION | Signal reconstruction | 94A12 | Edge detection | Non-uniform Fourier data | Sparse Bayesian learning | Regularization | 62F15 | Algorithms
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 10/2019, Volume 29, Issue 5, pp. 1440 - 1502
We study the problem of embedding arbitrary $${\mathbb {Z}}^k$$ Z k -actions into the shift action on the infinite dimensional cube $$\left( [0,1]^D\right)... 
Band-limited signal | {\mathbb {Z}}^k$$ Z k -action | Analysis | Embedding | Mathematics | Tiling of $${\mathbb {R}}^k$$ R k | Dynamical system | 37B05 | 54F45 | 94A12 | Mean dimension
Journal Article
Advances in Pure and Applied Mathematics, ISSN 1867-1152, 11/2014, Volume 5, Issue 4, pp. 243 - 253
The goal is to construct random frames and study properties of such frames. Starting with the construction of unimodular random sequences whose expected... 
random matrix | frames | Autocorrelation | sequences | 94A12 | 42C15 | Frames | Sequences | Random matrix
Journal Article
Journal Article
Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 02/2019, Volume 22, Issue 2, pp. 121 - 128
Sampling theorem is the theoretical basis of modern communication system, and is also one of the most powerful basic tools in signal processing and image... 
Mixed Lebesgue spaces | Shift invariant subspaces | 41A58 | Sampling theorem | 94A12 | 42C15 | 94A20
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 03/2017, Volume 38, Issue 3, pp. 395 - 407
In this article, we mainly study the periodic nonuniform dynamical sampling in ℓ 2 (ℤ) and shift-invariant spaces. We first provide a sufficient and necessary... 
Wiener amalgam space | Dynamical sampling | 41A58 | periodic nonuniform sampling | 94A12 | 42C15 | shift-invariant spaces | 94A20
Journal Article
Journal of Integral Equations and Applications, ISSN 0897-3962, 2014, Volume 26, Issue 4, pp. 455 - 481
In this paper,the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of uniform approximation for... 
Lipschitz classes | Multivariate sampling kantorovich operators | Irregular sampling | Order of approximation | Orlicz spaces | MATHEMATICS | MATHEMATICS, APPLIED | Multivariate sampling Kantorovich operators | order of approximation | irregular sampling
Journal Article
Journal of Information and Optimization Sciences, ISSN 0252-2667, 01/2019, Volume 40, Issue 1, pp. 81 - 95
This work introduces a signal watermarking scheme employing the fractional Fourier transform in the time-frequency domain. The proposed scheme employs an image... 
68U10 | 94A08 | Wigner Distribution | Image Watermarking | Fractional Fourier Transform | 94A12 | Spectrogram
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 01/2019, Volume 40, Issue 2, pp. 216 - 240
A probabilistic frame is a Borel probability measure with finite second moment whose support spans . A Parseval probabilistic frame is one for which the... 
frame operators | 60D05 | Parseval frames | Probabilistic frames | Wasserstein metric | 94A12 | 42C15 | MATHEMATICS, APPLIED | BASES | ADVENT | LIFE | Frames | Continuity (mathematics) | Statistical analysis
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 02/2019, Volume 35, Issue 2, pp. 245 - 256
In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the solution of... 
Cardinal spline interpolation | sampling set | nonuniform sampling | 94A12 | 42C15 | 94A20 | MATHEMATICS | MATHEMATICS, APPLIED | Reconstruction | Spline functions | Nonuniform | Splines | Mathematical analysis | Uniqueness
Journal Article
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