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A Simple Proof of the Restricted Isometry Property for Random Matrices
Abstract We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two mainExpand
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Constructive Approximation
Establishing Markov-type inequalities for the derivatives of poly-nomials with restricted zeros was initiated by P. Erdrs [3] in 1940. Since then several authors proved similar estimates for theExpand
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Compressed sensing and best k-term approximation
The typical paradigm for obtaining a compressed version of a discrete signal represented by a vector x ∈ R is to choose an appropriate basis, compute the coefficients of x in this basis, and thenExpand
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Adaptive wavelet methods for elliptic operator equations: Convergence rates
This paper is concerned with the construction and analysis of wavelet-based adaptive algorithms for the numerical solution of elliptic equations. These algorithms approximate the solution u of theExpand
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Adaptive Finite Element Methods with convergence rates
Summary.Adaptive Finite Element Methods for numerically solving elliptic equations are used often in practice. Only recently [12], [17] have these methods been shown to converge. However, thisExpand
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Degree of nonlinear approximation
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Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; inExpand
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Some remarks on greedy algorithms
Estimates are given for the rate of approximation of a function by means of greedy algorithms. The estimates apply to approximation from an arbitrary dictionary of functions. Three greedy algorithmsExpand
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Deterministic constructions of compressed sensing matrices
  • R. DeVore
  • Computer Science, Mathematics
  • J. Complex.
  • 1 August 2007
Compressed sensing is a new area of signal processing. Its goal is to minimize the number of samples that need to be taken from a signal for faithful reconstruction. The performance of compressedExpand
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Nonlinear approximation
This is a survey of nonlinear approximation, especially that part of the subject which is important in numerical computation. Nonlinear approximation means that the approximants do not come fromExpand
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