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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 main… Expand
Establishing Markov-type inequalities for the derivatives of poly-nomials with restricted zeros was initiated by P. Erdrs  in 1940. Since then several authors proved similar estimates for the… Expand
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 then… Expand
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 the… Expand
Adaptive Finite Element Methods with convergence rates
Summary.Adaptive Finite Element Methods for numerically solving elliptic equations are used often in practice. Only recently ,  have these methods been shown to converge. However, this… Expand
Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
- A. Chambolle, R. DeVore, Nam-Yong Lee, B. Lucier
- Mathematics, Computer Science
- IEEE Trans. Image Process.
- 1 March 1998
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; in… Expand
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 algorithms… Expand
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 compressed… Expand