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Compressive sensing
 IEEE Signal Processing Mag
, 2007
"... The Shannon/Nyquist sampling theorem tells us that in order to not lose information when uniformly sampling a signal we must sample at least two times faster than its bandwidth. In many applications, including digital image and video cameras, the Nyquist rate can be so high that we end up with too m ..."
Abstract

Cited by 687 (65 self)
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will learn about a new technique that tackles these issues using compressive sensing [1, 2]. We will replace the conventional sampling and reconstruction operations with a more general linear measurement scheme coupled with an optimization in order to acquire certain kinds of signals at a rate significantly
Compressed sensing
 IEEE Trans. Inf. Theory
, 2006
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
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Cited by 3600 (24 self)
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We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal
Bayesian Compressive Sensing
, 2007
"... The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing ..."
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Cited by 327 (24 self)
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The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing
Compressive Sensing
, 2010
"... Compressive sensing is a new type of sampling theory, which predicts that sparse signals and images can be reconstructed from what was previously believed to be incomplete information. As a main feature, efficient algorithms such as ℓ1minimization can be used for recovery. The theory has many poten ..."
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Cited by 50 (13 self)
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Compressive sensing is a new type of sampling theory, which predicts that sparse signals and images can be reconstructed from what was previously believed to be incomplete information. As a main feature, efficient algorithms such as ℓ1minimization can be used for recovery. The theory has many
Iterative hard thresholding for compressed sensing
 Appl. Comp. Harm. Anal
"... Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery probl ..."
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Cited by 324 (18 self)
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Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE Journal of Selected Topics in Signal Processing
, 2007
"... Abstract—Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined wi ..."
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Cited by 524 (15 self)
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with a sparsenessinducing (ℓ1) regularization term.Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution, and compressed sensing are a few wellknown examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound
Compressed Sensing and Redundant Dictionaries
"... This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry con ..."
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Cited by 140 (16 self)
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This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry
Compressive Sensing
"... •Compressive sensing (CS) is a sampling strategy for signals that are sparse in an arbitrary orthonormal basis Ψ. • It is a generalization of classic NyquistShannon sampling for signals that have a continuous finite support in Fourier basis.•Given a signal x ∈ RN = Ψw satisfying ‖w‖`0: = T  =  ..."
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•Compressive sensing (CS) is a sampling strategy for signals that are sparse in an arbitrary orthonormal basis Ψ. • It is a generalization of classic NyquistShannon sampling for signals that have a continuous finite support in Fourier basis.•Given a signal x ∈ RN = Ψw satisfying ‖w‖`0: = T
compressed sensing
, 2013
"... This paper discusses new bounds for restricted isometry property in compressed sensing. In the literature, E.J. Candès has proved that δ2s < √ 2 − 1 is a sufficient condition via l1 optimization having ssparse vector solution. Later, many researchers have improved the sufficient conditions on δ2 ..."
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This paper discusses new bounds for restricted isometry property in compressed sensing. In the literature, E.J. Candès has proved that δ2s < √ 2 − 1 is a sufficient condition via l1 optimization having ssparse vector solution. Later, many researchers have improved the sufficient conditions on δ
Compressed Sensing.
, 2011
"... The central problem of Compressed Sensing is to recover a sparse signal from fewer measurements than its ambient dimension. Recent results by Donoho, and Candes and Tao giving theoretical guarantees that ( 1minimization succeeds in recovering the signal in a large number of cases have stirred up mu ..."
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The central problem of Compressed Sensing is to recover a sparse signal from fewer measurements than its ambient dimension. Recent results by Donoho, and Candes and Tao giving theoretical guarantees that ( 1minimization succeeds in recovering the signal in a large number of cases have stirred up
Results 1  10
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