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Is face recognition really a compressive sensing problem
 in CVPR
, 2011
"... Compressive Sensing has become one of the standard methods of face recognition within the literature. We show, however, that the sparsity assumption which underpins much of this work is not supported by the data. This lack of sparsity in the data means that compressive sensing approach cannot be gua ..."
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Cited by 28 (3 self)
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Compressive Sensing has become one of the standard methods of face recognition within the literature. We show, however, that the sparsity assumption which underpins much of this work is not supported by the data. This lack of sparsity in the data means that compressive sensing approach cannot
An Alternating l1 approach to the compressed sensing problem
, 2009
"... Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined system of linear equations with the sma ..."
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Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined system of linear equations
1The Cognitive Compressive Sensing Problem
"... Abstract—In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying N dimensional random vector, by collecting at most K arbitrary projections of it. The N components of the latent vector represent subchannels states ..."
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Abstract—In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying N dimensional random vector, by collecting at most K arbitrary projections of it. The N components of the latent vector represent sub
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
The Two Stage l1 Approach to the Compressed Sensing Problem
, 2009
"... This paper gives new results on the recovery of sparse signals using l1norm minimization. We introduce a twostage l1 algorithm equivalent to the first two iterations of the alternating l1 relaxation introduced in [5] for an appropriate value of the Lagrange multiplier. The first step consists of t ..."
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Cited by 2 (0 self)
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This paper gives new results on the recovery of sparse signals using l1norm minimization. We introduce a twostage l1 algorithm equivalent to the first two iterations of the alternating l1 relaxation introduced in [5] for an appropriate value of the Lagrange multiplier. The first step consists of the standard ℓ1 relaxation. The second step consists of optimizing the ℓ1 norm of a subvector whose components are indexed by the ρm largest components in the first stage. If ρ is set to 1 4, an intuitive choice motivated by the fact that
A SECONDORDER METHOD FOR COMPRESSED SENSING PROBLEMS WITH COHERENT AND REDUNDANT DICTIONARIES
, 2014
"... Abstract. In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with nonsmooth and nonseparable regularization term, therefore a specialized solve ..."
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Abstract. In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with nonsmooth and nonseparable regularization term, therefore a specialized
A SECONDORDER METHOD FOR COMPRESSED SENSING PROBLEMS WITH COHERENT AND REDUNDANT DICTIONARIES
, 2014
"... Abstract. In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with nonsmooth and nonseparable regularization term, therefore a specialized solve ..."
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Abstract. In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with nonsmooth and nonseparable regularization term, therefore a specialized
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 ..."
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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
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
Compressive sampling
, 2006
"... Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired res ..."
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Cited by 1427 (15 self)
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resolution of the image, i.e. the number of pixels in the image. This paper surveys an emerging theory which goes by the name of “compressive sampling” or “compressed sensing,” and which says that this conventional wisdom is inaccurate. Perhaps surprisingly, it is possible to reconstruct images or signals
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